Question

This is one part to the question.Select the correct choice below and fill in the blank if necessary.

Answer 1

`\text{ There is one vertical asymptote. Its equation is x=2.}`

Explanation:

Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator.

If the degree of the denominator is equal to the degree of the numerator, there will be a horizontal asymptote at the ratio between the coefficients of the highest degree of the function. A horizontal asymptote at y = 0 means that the degree of the denominator is greater than the degree of the numerator

A vertical asymptote with a rational function occurs when there is division by zero.

Therefore, for the given function:

`f(x)=(7)/(x-2)`

Since for x=2 the denominator could be 0, there is a vertical asymptote at x=2.

Horizontal asymptote at y=0 means that the degree of the denominator is greater than the degree of the numerator.