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Exercises Exponentials and logarithms

Example 1 from Algebra and Trigonometry, 6.1 Exponential Functions

Identifying Exponential Functions

Which of the following equations are not exponential functions?

$f (x) = 4^{3 (x - 2)}$
$g (x) = x^{3}$
$h (x) = {(\frac{1}{3})}^{x}$
$j (x) = {(- 2)}^{x}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
By definition, an exponential function has a constant as a base and an independent variable as an exponent. Thus, $g (x) = x^{3}$ does not represent an exponential function because the base is an independent variable. In fact, $g (x) = x^{3}$ is a power function.

Recall that the base b of an exponential function is always a positive constant, and $b \neq 1.$ Thus, $j (x) = {(−2)}^{x}$ does not represent an exponential function because the base, $−2,$ is less than $0.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Which of the following equations represent exponential functions?

$f (x) = 2 x^{2} - 3 x + 1$
$g (x) = {0.875}^{x}$
$h (x) = 1.75 x + 2$
$j (x) = {1095.6}^{- 2 x}$

How did it go?

Next Evaluating Exponential Functions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.