Question

Which graph shows h(x) = f(x)/g(x)?

Answer 1

Answer: Third answer option.

Explanation:

To answer this question, we must pay careful attention to the way the graphs are labeled. Some things to note are linear functions have a degree of one, quadradic functions have a degree of 2, and rational functions will have a numerator and a vertical asymptote.

We are asked to find which graph shows
`h(x)=(f(x))/(g(x))`.

In the first option, we see that a rational function divided by a linear function results in a parabola. This is incorrect.

In the second option, we see a quadradic function divided by a linear function results in a linear function. This would be correct if the graphs went through the origin, but they do not.

In the third option, we see a quadradic function divided by a linear function gives a rational function. This is correct, since our graphs don't go through the origin (g(x) will give a vertical asymptote).

In the fourth option, we see a linear function divided by a linear function gives a quadratic function. This is incorrect.