Question 61021
Graph {{{f(x)=(4x+8)/(x^2-2x-15)}}} Indicate all intercepts and asymptotes.
The horizontal asymptote is y=0, because the degree of the numerator is less the the degree of the denominator.
:
The vertical asymptotes are when the denominator=0:
{{{x^2-2x-15=0}}}
(x-5)(x+3)=0
x=5 and x=-3 are vertical asymptotes.
:
The x-intercept happens when the numerator =0.
4x+8=0
4x=-8
4x/4=-8/4
x=-2  The x-intercept is (-2,0)
:
The y-intercept happens when x=0.
{{{f(0)=(4(0)+8)/(0^2-2(0)-15)}}}
{{{f(0)=8/-15}}}
The y-intercept (0,-8/15)
:
{{{graph(300,200,-10,10,-10,10,(4x+8)/(x^2-2x-15))}}}

Happy Calculating!!!