Unit 5: Functions This unit will introduce you to functions in general, operations on functions, and inverse functions. This is a very important unit especially for students that will be continuing to calculus. You will also learn about two very important functions: the exponential function and its inverse, the logarithmic function. You will also study various applications of these functions. The exponential function has many applications. One of the most common applications is to calculate compound interest.
Unit 5 Time Advisory
Completing this unit should take approximately 27.5 hours.
☐ Subunit 5.1: 4 hours
☐ Subunit 5.2: 4.5 hours
☐ Subunit 5.3: 4.5 hours
☐ Subunit 5.4: 3 hours
☐ Subunit 5.5: 3 hours
☐ Subunit 5.6: 4 hours
☐ Subunit 5.7: 4.5 hours
Unit5 Learning Outcomes
Upon successful completion of this unit, you will be able to:
- determine the domain of a function;
- evaluate functions at numerical and variable inputs;
- evaluate a sum, product, difference, and quotient of functions at
numerical and variable inputs;
- compute the composition of two functions;
- determine the inverse of a function;
- graph quadratic functions by identifying key points;
- find compound and continuous interest; and
- solve exponential and logarithmic equations.
5.1 Functions
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.1: Function
Notation”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.1: Function
Notation” (PDF)
Instructions: Read Section 10.1 in Chapter 10 of your textbook,
pages 386–392, to learn about functions and functional notation.
Functions are relations between two variables (in general denoted by
x and y, where x is the independent variable and y is the dependent
variable) such that for each value of x there is only one value of
y. Note that this reading covers the topics in Subunits
5.1.1–5.1.4.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be
found here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Functions”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab
Notebook: “Functions”
(PDF)
Instructions: Complete pages 96–99 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.1.1–5.1.4, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.1.1 Definition and Vertical Line Test of Functions Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions
– Definition and Vertical Line Test”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions –
Definition and Vertical Line
Test” (YouTube)
Instructions: Watch the video linked above, which discusses the definition of a function as well as the vertical line test. Functions are relations between two variables (in general denoted by x and y, where x is the independent variable and y is the dependent variable) such that for each value of x there is only one value of y. If a relationship between x and y is graphed, one can determine if the relationship is a function by using the vertical line test. The graph represents a function if every vertical line intersects the graph at most once.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.1.2 Domain of a Function Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions
– Domain”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions –
Domain” (YouTube)
Instructions: Watch the video linked above, which explains the notion of the domain of a function. The domain of this function contains all values that can replace x such that you can calculate y. Speaking geometrically, this means all values of x such that a vertical line through x will intersect the graph.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.1.3 Function Notation Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions
– Function Notation”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions –
Function Notation”
(YouTube)
Instructions: Watch the video linked above, which discusses function notation. The explicit function notation is f(x), so you write y = f(x), which means y is a function of x. This is a convenient notation to explicitly define a function and evaluate. For instance, to write y = f(3) means “what is y when x = 3?”
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.1.4 Function Evaluation at Expression Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions
– Evaluate at Expression”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions –
Evaluate at
Expression” (YouTube)
Instructions: Watch the video linked above, which discusses evaluating a function at an algebraic expression. In the last video, you saw how to evaluate at a number, say f(3) for instance. Using the same concept, you can evaluate at an algebraic expression, for instance f(x+3).
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.2 Algebra of Functions
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.2: Operations on
Functions”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.2: Operations on
Functions” (PDF)
Instructions: Read Section 10.2 in Chapter 10 of your textbook,
pages 393–400, to learn the algebra of functions. As in arithmetic,
you can add, subtract, multiply, and divide functions. There is an
additional but important operation called composites. A composite of
a function with another function is a function at the second
function. You write (f_{°}g)(x) = f(g(x)). Note that this
reading covers the topics in Subunits 5.2.1–5.2.3.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Algebra of Functions”
Link: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Algebra
of
Functions”
(PDF)
Instructions: Complete pages 100–101 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.2.1–5.2.3, and then review the worksheet as you follow along with the videos for solutions.
Reading this section and taking notes should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.2.1 Add/Subtract/Multiply/Divide Functions (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions – Add/Subtract/Multiply/Divide (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions – Add/Subtract/Multiply/Divide (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses the arithmetic of functions. In a very natural way, you can add, subtract, multiply, and divide functions. This video gives examples of each.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.2.2 Add/Subtract/Multiply/Divide Functions (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions – Add/Subtract/Multiply/Divide (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions – Add/Subtract/Multiply/Divide (Part
2)” (YouTube)
Instructions: Watch the video linked above, which provides another example of the basic arithmetic of functions.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.2.3 Composition of Functions Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions – Composition”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of
Functions –
Composition”
(YouTube)
Instructions: Watch the video linked above, which discusses composition of functions. You can compose functions and use the circle to indicate this. You write (f_{°}g)(x) = f(g(x)).
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.3 Inverse Functions
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.3: Inverse
Functions”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.3: Inverse
Functions”
(PDF)
Instructions: Read Section 10.3 in Chapter 10 of your textbook,
pages 401–405, to learn about inverse functions. Knowing the inverse
function of a function can be very helpful in solving many equations
in the same way it is helpful to understand that subtraction is the
inverse of addition and squaring is the inverse of square root. Note
that this reading also covers the topics in Subunits 5.3.1–5.3.3.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Inverse Functions”
Link: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Inverse
Functions”
(PDF)
Instructions: Complete pages 102–104 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.2.1–5.3.3, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.3.1 Determine If Functions Are Inverses Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Showing Functions Are Inverses”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Showing Functions Are
Inverses” (YouTube)
Instructions: Watch the video linked above, which discusses how to determine if a function is the inverse of another function. The inverse function undoes what a function does to a value of x. For instance, if f(x) = x + 3, then g(x) = x - 3 is the inverse. The test to determine the inverse is (f_{°}g)(x) = (g_{°}f)(x) = x.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.3.2 Find the Inverse of a Function Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Find the Inverse”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Find the
Inverse” (YouTube)
Instructions: Watch the video linked above, which discusses how to find the inverse of a function. If y = f(x) is the function, then the inverse function, denoted by f^{-1}(x), can be found by solving for x and then replacing y with x and x with y.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.3.3 Graph the Inverse of a Function Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Graph the Inverse”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse
Functions – Graph the
Inverse” (YouTube)
Instructions: Watch the video linked above, which illustrates how to graph the inverse of a function. The inverse of a function is interchanging the role of the x and y. Graphically, this means that the graph of an inverse function is a reflection across the line y = x.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.4 Graph Quadratic Functions
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 9, Section 9.11: Graphs of
Quadratics”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 9, Section 9.11: Graphs of
Quadratics”
(PDF)
Instructions: Read Section 9.11 in Chapter 9 of your textbook,
pages 380–384, to learn the characteristics of the graphs of
quadratics. When graphed, the quadratic function has several
characteristics. Each quadratic function graph has a vertex (a point
where the graph stops going down and starts going up or vice versa),
a line of symmetry, and a maximum value or a minimum value. Note
that this reading covers the topics in Subunits 5.4.1 and 5.4.2.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Graph Quadratic Functions”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Graph Quadratic
Functions”
(PDF)
Instructions: Complete page 105 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.4.1 and 5.4.2, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.4.1 Graph Key Points of Quadratic Functions (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Graph
Quadratic Functions – Key Points (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Graph
Quadratic Functions – Key Points (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses the key points of the graph of the quadratic function. This video describes what direction the graph is (either U shaped or up-side-down U shaped), the y-intercept, the x-intercept, and the vertex of the graph.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.4.2 Graph Key Points of Quadratic Functions (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Graph
Quadratic Functions – Key Points (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Graph
Quadratic Functions – Key Points (Part
2)” (YouTube)
Instructions: Watch the video linked above, which gives an additional example of finding key points on the graph of the quadratic function.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.5 Exponential Functions
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.4: Exponential
Functions”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.4: Exponential
Functions”
(PDF)
Instructions: Read Section 10.4 in Chapter 10 of your textbook,
pages 406–409, to learn about exponential functions. The exponential
function is very important for many applications, but the most
common application is for certificate of deposits calculations. Note
that this reading also covers the topics in Subunits 5.5.1–5.5.2.
Reading this section and taking notes should take approximately 2
hours.
Termsof Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Exponential Equations and Exponential Functions” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Exponential Equations and Exponential Functions” (PDF)
Instructions: Complete pages 106–107 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.5.1 and 5.5.2, and then review the worksheet as you follow along with the videos for solutions.Completing this assessment should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.5.1 Exponential Equations with a Common Base Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Exponential Equations – Common Base”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential
Equations – Common
Base” (YouTube)
Instructions: Watch the video linked above, which discusses exponential equations with a common base. When an equation consisting of two exponential expressions has the same base and the unknown value is in the exponent, then the exponents must be equal.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.5.2 Exponential Equations with Binomial Exponents Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Exponential Equations – Binomial Exponents”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential
Equations – Binomial
Exponents” (YouTube)
Instructions: Watch the video linked above, which gives another example of an equation with a common base and equating the exponents.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.6 Compound Interest
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.6: Application:
Compound Interest”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.6: Application: Compound
Interest”
(PDF)
Instructions: Read Section 10.6 in Chapter 10 of your textbook,
pages 414–419, to learn an application of the exponential functions,
namely compound interest. A bank has certificates of deposits (CDs)
for sale. The interest rate paid is determined by the length of time
that the consumer chooses. The bank will compound the interest
(calculate the interest, and then pay interest on this interest)
during various intervals of time (quarterly, monthly, annually).
Once all of these parameters are known, the compound formula
calculates the return on your CD. Note that this reading also covers
the topics in Subunits 5.6.1–5.6.4.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Compound Interest”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Compound
Interest”
(PDF)
Instructions: Complete pages 108–111 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.6.1–5.6.4, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.6.1 Compound Interest with N Compounds per Year Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – N Compounds”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – N Compounds”
(YouTube)
Instructions: Watch the video linked above, which discusses an application of the exponential function, namely compound interest. The video gives the formula for return of money (future value of your money) and gives an example.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.6.2 Finding the Principle (P) Given the Return Amount (A) Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – Find Principle”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – Find
Principle” (YouTube)
Instructions: Watch the video linked above, which reverses the equation discussed above. These examples ask, knowing how much money you want returned, how much do you need to invest?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.6.3 Continuous Compounding Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – Continuous Compounds”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Interest – Continuous
Compounds” (YouTube)
Instructions: Watch the video linked above, which discusses an application of the exponential function, namely continuous compounding interest. Continuous compounding means the bank is compounding every millisecond of every day. When this happens, a new constant is introduced: e. e is a constant and is approximately equal to 2.7182818. Then the formula becomes A = Pe^{rt}.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.6.4 Finding the Principle (P) for Continuous Compounding Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.
Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Finding Principle with Continuous Interest” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Finding Principle with Continuous Interest” (YouTube)
Instructions: Watch the video linked above, which asks the reverse of the examples above for continuous compound interest. This video illustrates how to calculate the amount needed to invest when given how much one earns.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.7 Logarithms (Logs)
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 10, Section 10.5: Logarithmic
Functions”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 10, Section 10.5: Logarithmic
Functions”
(PDF)
Instructions: Read Section 10.5 in Chapter 10 of your textbook,
pages 410–413, to learn about logarithmic functions. The logarithmic
functions are the inverse functions to the exponential. Thus, these
functions become important when needing to solve an exponential
equation with the unknown in the exponent. Logarithmic functions
have many real-world applications. When the magnitude of an
earthquake is reported, the report does not give the actual tremor,
since this is a very large number. The report gives the log of the
tremor. The same is true for reporting sound (decibels) and acidity
(ph). Note that this reading also covers the topics in Subunits
5.7.1–5.7.3.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Logs”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab
Notebook: “Logs”
(PDF)
Instructions: Complete pages 112–114 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.7.1–5.7.3, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
5.7.1 Converting Logarithms Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs –
Convert”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs –
Convert” (YouTube)
Instructions: Watch the video linked above, which discusses how to convert from a logarithmic expression (log) to an exponential expression and vice versa. The conversion formula is: b^{x} = a is equivalent to log_{b}a = x.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.7.2 Evaluating Logarithms Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.
Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Evaluate” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Evaluate” (YouTube)
Instructions: Watch the video linked above, which discusses evaluating logarithmic expressions. For general bases (bases other than 10 and e which are on all scientific calculators), determining the value of a log may be easier to convert to an exponential expression. Then you can use previous learned techniques to solve the exponential equation. Thus, convert log_{b}a = x to b^{x} = a. Then use the techniques you learned in Subunit 5.5.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
5.7.3 Solving Logarithmic Equations Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs –
Solving”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs –
Solving” (YouTube)
Instructions: Watch the video linked above, which discusses solving logarithmic equations. As in the previous video, solving logarithmic equations is easier if first converted to an exponential equation.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
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Final Exam - Final Exam: The Saylor Foundation‘s “MA004 Final Exam” Link: The Saylor Foundation‘s “MA004 Final Exam”
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