Find the following for this function: f(x)=(2x^2-2)/(x^2-4x). a)List x and y intercepts if any exist. b)Give the equations for any possible vertical, horizontal, and slant asymptotes. c)Draw a sketch.

Question

Please answer my question and show me how you got it as soon as you can.

Answer 1

a) x intercepts are x=- 1 and x=1. take the numerator and set equal to zero x^2-1 = 0, x=+sqr1 = +1

no y intercepts. set x=0 and solve for y. that leads to division by zero. So, no solution, no y intercept

b) x=4 and x= 0 are vertical asymptote. Set the denominator =0. x^2-4x = x(x-4)=0 x-4=0, x=0

y=2 is a horizontal asymptote. look at the ratio of the coefficients of the x^2 terms. 2/1 = 2