This video tutorial explains how to determine slant asymptotes of rational functions. It assumes prior knowledge of vertical and horizontal asymptotes. The video covers the conditions under which a rational function has a slant asymptote and demonstrates how to find it using long division. Two examples are provided: the first focuses on identifying all asymptotes and graphing the function, while the second includes a hole in the function. The video concludes with a reminder to check for holes when using graphing software.

What is a slant asymptote in the context of rational functions?

• A line that the graph never approaches

• A vertical line that the graph approaches

• A slanted line that the graph approaches

• A horizontal line that the graph approaches

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CCSS.HSF-IF.C.7D

Under what condition does a rational function have a slant asymptote?

• When the degree of the numerator is equal to the degree of the denominator

• When the degree of the numerator is one less than the degree of the denominator

• When the degrees of the numerator and denominator are both zero

• When the degree of the numerator is one more than the degree of the denominator

Tags

CCSS.HSF-IF.C.7D

What is the first step in determining all asymptotes of a rational function?

• Factor the given function

• Find the y-intercept

• Perform long division

• Graph the function

Tags

CCSS.HSF-IF.C.7D

In the first example, what is the vertical asymptote of the function?

• x = 2

• x = 1

• x = -1

• x = 0

Tags

CCSS.HSF-IF.C.7D

What is the equation of the slant asymptote in the first example?

• y = -1/2x + 1

• y = 2x - 1

• y = 1/2x + 1

• y = x + 1

Tags

CCSS.HSF-IF.C.7D

In the second example, what is identified as a hole in the function?

• x = 1

• x = 2

• x = 0

• x = -1

Tags

CCSS.HSF-IF.C.7D

What is the equation of the slant asymptote in the second example?

• y = 2x

• y = x - 1

• y = x

• y = -x

Tags

CCSS.HSF-IF.C.7D

What is the importance of factoring in determining asymptotes?

• It determines the slope of the asymptote

• It simplifies the function for easier division

• It is not important

• It helps in finding the y-intercept

Tags

CCSS.HSF-IF.C.7D

Why might software not show holes in the graph of a function?

• Because holes do not exist in rational functions

• Because the screen lacks enough definition

• Because the function is not simplified

• Because the software is outdated

Tags

CCSS.HSF-IF.C.7D

What should you check on your graphing calculator to identify holes?

• The graph

• The equation

• The table

• The settings

Tags

CCSS.HSF-IF.C.7D