Graphs of Exponential Functions $f\left(x\right)=b^x$
Consider the following graphs:
$f\left(x\right)=2^x$  $f\left(x\right)=\left(\frac{1}{3}\right)^x$ 



We could look at more examples, and end up with the following rules, for the graph of an exponential function $f\left(x\right)=b^x$:
Graphs of Exponential Functions $f\left(x\right)=a \cdot b^x$
Consider the following graphs:
$f\left(x\right)=3 \cdot 2^x$  $f\left(x\right)=2 \cdot \left(\frac{1}{3}\right)^x$ 



So far so good, but what if $a<0$?
$f\left(x\right)=2 \cdot 3^x$  


Graphs of Exponential Functions $f\left(x\right)=a \cdot b^x$
$a$ positive  $a$ negative  

$0 \lt b \lt 1$  decreasing  increasing 
$b>1$  increasing  decreasing 