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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The vertical asymptote is at x = -1.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The hole is at x = 2.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D