Exercise 16 Page 966

We are given the graph of a rational function. Let's take a look at it by considering its vertical asymptote.

Since the vertical asymptote of the function lies at $x=\text{-}3,$ the function is undefined for $x=\text{-}3.$ By knowing this we can write the denominator of our rational equation. We need to have $(x+3)$ as a product in the denominator. Knowing this, we can eliminate options F and H. Now, let's write our partial equation considering the remaining options G and I. Since the graph passes through the origin, we will substitute $x=0$ and $y=0$ into the above equation to determine the value of $b.$ With the value of $b$ as $0,$ we can eliminate option G. Although we can now conclude that the answer is option I, let's check it by finding the value of $a.$ To do so we will use another point from the graph, $(\text{-}2,\text{-}2).$ Great! Now, we can complete our function. Therefore, the answer is option I.