Question

guided practice
remember that when plotting points, it is most helpful to use three or more values of x on each side of the vertical asymptote.
rational functions
given a vertical asymptote at x = 0 and a horizontal asymptote at y = 2, which values of x should be used to determine coordinates?
a. y = -1, 0, 1, 3, 4, 5
b. x = -3, -2, -1, 0, 1, 2
c. x = -3, -2, -1, 1, 2, 3
d. y = -1, 0, 1, 2, 3, 4

Explanation:

The vertical asymptote is at \(x=0\), so \(x=0\) cannot be used (it makes the function undefined). We need x-values on both sides of \(x=0\) (negative and positive non-zero values). Option C includes negative values (-3,-2,-1) and positive values (1,2,3) without 0, which fits the requirement. Other options either include 0 (B) or use y-values (A,D) instead of x-values.

Answer:

C. x=-3,-2,-1,1,2,3