6Given rx x24x5x3 a Find the xintercepts b Find the yinterc

6)Given r(x) = x^2-4x-5/x-3

a) Find the x-intercept(s)

b) Find the y-intercept.

c) Find the asymptotes. Label the asymptotes as vertical, horizontal or slant asymptote.

f(x)= (x²-4x-5)/(x-3)

a. x- intercept

To find the x- intercept,we have to plug f(x)=0

(x²-4x-5)/(x-3)=0

(x-5)(x+1)=0

x=5,-1

Therefore x-intercepts are (5,0),(-1,0)

b. y-intercept

To find the y-intercept,we have to plug x=0

y=(0-4(0)-5)/(0-3)= 5/3

Therefore y intercept is (0,5/3)

c. Vertical asymptote

TO find VA,we have to set the bottom to zero

x-3=0

x=3

There is no horizontal asymptote

And to find the slant asymptote we have to divide numerator by the denominator

y=(x²-4x-5)/(x-3)

y= (x-1) -8/(x-3)

Slant asymptote,y= x-1