### Home > PC3 > Chapter 8 > Lesson 8.1.1 > Problem8-13

8-13.

Copy and complete the following table for $g(x)=a^x$, where $a>0$.

g(x) = ax

0 < a < 1

a > 1

Example sketch

$\lim \limits _ { x \rightarrow \infty } g ( x )$

$\lim \limits _ { x \rightarrow - \infty } g ( x )$

g(x) = a

0 < a < 1

a > 1

Example sketch

$g\left(x\right)=\left(\frac{1}{2}\right)^x$

$g\left(x\right)=2^x$

$\lim \limits _ { x \rightarrow \infty } g ( x )$

$\lim \limits _ { x \rightarrow - \infty } g ( x )$

The first curve is exponential decay. The second is exponential growth.