Rational Function: finding x and y intercepts and asymptotes.

Question

(x^2-9)/(x+5). Please show work on finding the x and y intercept and asymptotes.

Answer 1

Plug in x=0 to find the y-intercept:

(0^2-9)/(0+5) = -9/5

The y-intercept is (0, -9/5)

Find where y=0 for the x-intercept. y=0 when the numerator is 0.

x^2-9 = 0

x = ±3

The x-intercepts are (-3,0) and (3,0).

There are vertical asymptotes where the denominator is 0.

x+5 = 0

x=-5

There are no horizontal asymptotes because the degree of the numerator is greater than the degree of the denominator.