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= - 3, the function is undefined for x= - 3. By knowing this we can write the denominator of our rational equation.
x=- 3 ⇔ x+3=0We 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.
f(x) = ax+ b/x+3
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, ( -2, -2).
