Find the intercepts and asymptotes

Question

r(x)= 2x-2/x+2

x- intercept (x,y)= ?

y- intercept (x,y)= ?

vertical asymptote(s) =?

horizontal asymptote=?

sketch a graph of the rational function.

Answer 1

Along the x-axis, y = 0.

2x - 2 = 0

2x = 2

x = 1

(1,0)

Along the y-axis, x = 0.

2(0) - 2/0 + 2 = -2/2 = -1

(0,-1)

Our denominator can't be 0. What values of x make the denominator 0?

x + 2 = 0

x = -2

This is the vertical "line" we can't touch, or else our fraction is undefined, our vertical asymptote.

The horizontal asymptote is the horizontal "line" our graph approaches as x gets bigger and bigger. Since the lead degrees of the numerator and denominator are the same, we look at 2x/x, which equals 2.

y = 2