Question

Write a function with the following characteristics: 1.A vertical asymptote at x = 3 A horizontal asymptote at y = 2 An x-intercept at x=-5 2.A vertical asymptote at x=-1 An oblique asymptote at y = x + 2

Answer 1

1. The vertical asymptote requires the denominator have a zero at that location. The x-intercept requires the numerator have a zero at that location. The horizontal asymptote amounts to a multiplier of the function:

... y = 2(x +5)/(x -3)

2. The vertical asymptote requires the denominator have a zero at that location. The oblique asymptote is an add-on

... y = 1/(x +1) +(x +2)

... y = (x² +3x +3)/(x +1)