Question

use a graphing calculator to obtain the graph of the function. What do you observe about its asymptotes?

g(x) = 4 [x-2] / x + 1

My answer was there are two horizontal asymptotes. My teacher said that there are two asymptotes but she wants me to find the equation for them. I do not understand what she means.

Answer 1

If x is alone at the bottom, you have vertical asymptotes at x = 0
if (x+1) is on the bottom, they are at x = -1
There are no horizontal asymptotes here.

Answer 2

x = 0 is the equation of a vertical asymptote for example, graph it.

Answer 3

I have to disagree with Damon, although he is usually right.

If your equation is
y = 4(x-2)/(x+1) there is a horizontal asymptote of
y = 4

If you equation is
y = 4(x-2)/x + 1 as you typed it,
there is a horizontal asymptote of
y = 5

Answer 4

Sorry. I only really looked at the x singularity.
Of course if x gets big positive or negative y approaches 4 (x/x) if you have (x-2)/(x+1)