Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

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461–465 Identify all vertical and oblique asymptotes.

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466–480 Sketch the graph of the rational function, indicating all intercepts and asymptotes.

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Chapter 9

Exponential functions are inverses of logarithmic functions — and vice versa. Working with exponential and logarithmic functions requires facility with the correspondence and interrelationship between them. The base of an exponential function must be positive; many mathematicians also exclude the number 1 from being a base. A logarithmic function can have any positive base except the number 1, and the argument (input value) of a logarithmic function must also be positive.

In this chapter, you’ll work with exponential and logarithmic functions in the following ways:

Evaluating exponential and logarithmic expressions

Using the laws of logarithms

Sketching exponential and logarithmic functions

Solving for the function’s inverse

Solving exponential equations

Solving logarithmic equations and checking for extraneous roots

Don’t let common mistakes trip you up; remember the following ones when working with exponential and logarithmic functions:

Not using the order of operations properly when evaluating exponential expressions

Writing a binomial argument (input statement) incorrectly — splitting it up

Using laws of logarithms incorrectly

481–490 Evaluate the exponential functions for the input values indicated.

481. If

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487. If

488. If