Chapter 4, Problem 1RE

To determine

Match equation with the letter of the graph that most closely resemble the graph of the equation.

Answer to Problem 1RE

Solution:

The graph of the function is match with the option (c).

Given:

The function: $y=a^{x+2}$, assume that $a>1$.

Explanation of Solution

Consider the function:

$y=a^{x+2}$

Simplify above equation as follows:

$\begin{array}{c}y=a^{x+2}\\ =a^x\times a^2\end{array}$

Now, begin with the graph of $y=a^x$.

When $x=0$ then $y=a^2$. So, the graph has $y-\text{intercept}$ is $a^2$.

So, the graph of the function is:

The graph of the function is match with the option (c).