Asymptote and Holes Practice

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of a rational function equal to zero and solve for x.

Front

What is a hole in a graph?

Back

A hole is a point where a function is not defined due to a common factor in the numerator and denominator that cancels out.

Front

How do you find holes in a function?

Back

To find holes, factor the numerator and denominator, identify common factors, and set them equal to zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, y = 0. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What does it mean if a function has no horizontal asymptote?

Back

It means that as x approaches infinity or negative infinity, the function does not approach a specific y-value.

Front

Given the function f(x) = (x-2)/(x+1), find the vertical asymptote.

Back

The vertical asymptote is at x = -1.

Front

Given the function f(x) = (x^2 - 4)/(x - 2), find the hole.

Back

The hole is at x = 2.

Front

What is the significance of identifying asymptotes and holes in a function?

Back

Identifying asymptotes and holes helps understand the behavior of the function, including limits and discontinuities.