Answer:
D
Step-by-step explanation:
Rational functions are functions whose main operation on the variable is a ratio or fraction. This means we find x or the input value in the denominator of the function. Since fractions involve division and division has special circumstances, this reflects on the graph. Because when we divide we cannot divide by 0, any x value which makes the denominator 0 is an asymptote. On the graph, asymptotes are represented by dashed lines where the function doesn't follow.
To find the asymptotes, we set the factors in the denominator to 0 and solve for x. Let's do the each for each options:
a. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
b. x=0 and x+5=0 so x=-5. This does not match the graph.
c. x=0. This does not match the graph.
d. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.
This means only a and d are options. We will substitute a value to see the behavior of the graph. We pick x=-2. In D, this would give us a positive y. This matches the graph. In A, this would give us a negative y which does not match the graph.
