MATH 180 – STUDY GUIDES – Chapter 5 - 6TH EDTION
Section 5.1 – Composite Functions
1. Evaluate composite functions
2. Find the composite function and its domain (rational functions included)
3. Solve word problems involving composition of functions
4. Given a function H, find functions F and G so that H = F o G
Section 5.2 – Inverse Functions
5. Determine whether the function is one to one (From an equation)
6. Find the inverse of one to one functions
From a graph
From an equation (rational functions included)
7. Given the graph of a one to one function, sketch the graph of its inverse
8. Given a pair of inverse functions, show that their composition is x
9. State the domain and range of a function and its inverse
10. Solve word problems involving inverse functions
Section 5.3 – Exponential Functions (study boxed in problems 91-100 page 285)
11. Evaluate exponential expressions with the calculator
12. Recognize tables of exponential functions and write the corresponding function
13. Sketch the basic exponential functions and give domain, range, intercepts, and asymptotes
(
f ( x)  a * b x , for
b  1 , and for 0  b  1 ). (base e also included)
14. Sketch the graph of exponential functions using transformations and give domain, range, intercepts, and
asymptote (basic problems)
15. Solve exponential equations in which both sides can be written as a power of the same number
16. Solve word problems involving exponential functions (Evaluation type)
17. Find inverses of exponential functions and give domain and range of each
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Section 5.4 – Logarithmic Functions (study boxed in problems 111-116 page 299)
18. Change an exponential expression to an equivalent logarithmic expression
19. Change a logarithmic expression to an equivalent exponential expression
20. Evaluate logarithmic expressions with and without the calculator
21. Find the domain of a logarithmic function
22. Sketch the basic logarithmic functions and give domain, range, intercepts, and asymptote
( f ( x)  logb x ,for b  1 , and for 0  b  1 )
23. Sketch the graph of logarithmic functions using transformations and give domain, range, intercepts, and
asymptote
24. Solve exponential and logarithmic equations
25. Solve word problems involving logarithmic and exponential functions
a) Evaluation type and
b) Equation type
26. Find inverses of logarithmic functions and give domain and range of each
Section 5.5 – Properties of Logarithms (study boxed in problems 85-86 page 309)
27. Evaluate logarithmic expressions without the calculator
28. Write a logarithmic expression as a sum or difference of logarithms (expand using properties of
logarithms)
29. Write an expression as a single logarithm
30. Evaluate logarithms by using the change of base formula
31. Graph logarithmic functions with the calculator using the change of base formula
32. Solve logarithmic equations and express y as a function of x
Section 5.6 – Logarithmic and Exponential Equations (study boxed in problems 87-96 page 316)
33. Solve exponential equations: Steps: Isolate the exponential expression
Solve by using logs
34. Solve logarithmic equations: Steps: Take to format Log  = Log O, or Log  = # (any base)
Solve by exponentiation (with the same base)
35. Solve exponential and logarithmic equations with the calculator
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Section 5.8 – Applications
In all the following types word problems you should be able to
a) Construct the equation satisfying the given conditions
(That is, find the constants of the equation)
b) Answer the two kinds of problems:
a) Given x, find y (Evaluation type)
b) Given y, find x (Equation type)
c) Find intercepts and interpret within context
d) Find asymptotes and interpret within context
36. Word problems about uninhibited growth
Also, find the growth rate, and the doubling time
37. Word problems about uninhibited decay
Also, find decay rate, and the half-life
38. Word problems using the Newton’s law of cooling
Also, find asymptote and interpret within context
39. Word problems using the logistic model (optional)
Also, find carrying capacity, inflection point, asymptotes
Recognize the increasing and the decreasing case
Section 5.9 – More Applications
(OYO – similar to linear regression procedure: Sketch scatter-diagram with calculator, identify the function
and use the corresponding regression in the calculator)
40. Using regression analysis in the calculator to find the
a) Exponential model
b) Logarithmic model
c) Logistic model
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