Question

How do you graph `f(x)=-1/(x-2)` using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer 1

There is a vertical asymptote at `x=2`, a horizontal asymptote at `y=0` (x-axis) , no holes and no x-intercepts.

Explanation:

Analytically:

Setting the numerator = `0` gives x-intercepts. There are no factors in the numerator, so there are no x-intercepts.

Setting the denominator =`0` yields vertical asymptotes:
`x-2=0` yields a vertical asymptote at `x=2`

Horizontal asymptotes are found based on the degree of the numerator and denominator. If the degree of the numerator is one less than the degree of the denominator, the horizontal asymptote is the x-axis (`y=0`)

Since there is no variable in the numerator, the degree = 0.
The degree of the denominator is 1.

From the graph:
graph{-1/(x-2) [-10, 10, -5, 5]}