Graphing Rational Functions: Asymptotes and Intercepts

This video tutorial covers how to graph rational functions, including finding asymptotes, intercepts, and identifying holes. It provides a step-by-step process through five examples, demonstrating how to factor functions, analyze vertical and horizontal asymptotes, and perform sign analysis. The video also explains how to handle special cases like slant asymptotes and functions with no vertical asymptotes.

What is the first step in graphing a rational function?

• Find the intercepts

• Factor the rational function

• Plot additional points

• Determine the domain

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CCSS.HSF-IF.C.7D

What does it mean if a factor in the numerator cancels with a factor in the denominator?

• There is no intercept

• There is a horizontal asymptote

• There is a hole in the graph

• There is a vertical asymptote

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CCSS.HSF-IF.C.7D

How do you determine the vertical asymptotes of a rational function?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Plot the intercepts

• Find the highest power term

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CCSS.HSF-IF.C.7D

What is the horizontal asymptote if the degree of the denominator is higher than the degree of the numerator?

• y = 1

• y = x

• y = -1

• y = 0

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CCSS.HSF-IF.C.7D

In the second example, what is the x-coordinate of the hole?

• Negative 3

• 2

• 4

• 3

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CCSS.HSF-IF.C.7D

How do you find the y-coordinate of a hole in a rational function?

• Find the intercepts

• Plug the x-coordinate of the hole back into the simplified function

• Set the denominator equal to zero

• Set the numerator equal to zero

Tags

CCSS.HSF-IF.C.7D

How do you determine if a rational function has a slant asymptote?

• The degree of the denominator is one higher than the degree of the numerator

• The degrees of the numerator and denominator are equal

• The degree of the numerator is one higher than the degree of the denominator

• There are no vertical asymptotes

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CCSS.HSF-IF.C.7D

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

• y = 2x + 7

• y = x + 4

• y = 3x + 1

• y = x - 3

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CCSS.HSF-IF.C.7D

In the fourth example, why are there no vertical asymptotes?

• The denominator has no real roots

• The numerator is higher than the denominator

• There are holes in the graph

• The numerator and denominator are equal

Tags

CCSS.HSF-IF.C.7D

What is the y-intercept of the function in the fifth example?

• 3

• 2

• 1

• 0