Graphs of Exponential Functions

1. $3^x$ $\text{is}$ $\text{always}$ $\text{positive,}$ $\text{and}$ $\text{never}$ $0.$
2. $\text{Times}$ $-3\text{,}$ $\text{every}$ $\text{output}$ $\text{is}$ $\text{negative}:y<0.$

Answer: $y<0$

1. $2^x$ $\text{gets}$ $\text{closer}$ $\text{and}$ $\text{closer}$ $\text{to}$ $0$ $\text{as}$ $x$ $\text{decreases}\text{,}$ $\text{but}$ $\text{never}$ $\text{reaches}$ $\text{it.}$
2. $\text{So}$ $5$ $\text{times}$ $\text{it}$ $\text{approaches}$ $0\text{:}$ $\text{the}$ $\text{asymptote}$ $\text{is}$ $y=0.$

Answer: $y=0$

1. $a$ $\text{is}$ $\text{the}$ $\text{value}$ $\text{at}$ $x=0:a=4\text{.}$
2. $\text{Two}$ $\text{steps}$ $\text{multiply}$ $\text{by}$ $b$ $\text{twice:}$ $b^2=\frac{36}{4}=9\text{,}$ $\text{so}$ $b=3\text{.}$

Answer: $y=4(3{)}^x$