Exercise 14 Page 965

We are asked to write a function to represent the following graph.

Notice that this is a graph of an exponential function. Therefore, it needs to be in the following form. In this form $a$ represents the $y\text{-}$intercept. As we can see from the graph, our $y\text{-}$intercept is $\text{-}2.$ Therefore, the value of $a$ is $\text{-}2.$ If we examine the given options we can see that all $b$ values are $3.$ By knowing this we will examine the remaining two options G and I by checking for an arbitrary point. Let's randomly choose $x=\text{-}4$ and then substitute into these options to see the corresponding outputs. Let's begin with option I. We can see from the graph that the value of $\text{-}4$ is approximately $0.$ Therefore, we can eliminate option I also. Last, let's check option G. Great! We get approximately $0$ for the value of $f(\text{-}4).$ We can conclude that our exponent needs to be positive $x.$ Therefore, our answer is option G.