Rational Transformations Holes Asymptotes Domain Range

What is a rational function?

• A function that is a fraction of polynomials p(x) and q(x)

• A function that is a product of polynomials p(x) and q(x)

• A function that is a sum of polynomials p(x) and q(x)

• A function that is a difference of polynomials p(x) and q(x)

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CCSS.HSF-IF.C.7D

The domain of a rational function is the set of all real numbers except the roots of the ​ (a)   polynomial.

• denominator
• numerator

x-intercepts, also known as roots, are the points where the graph of a rational function meets the x-axis and are the roots of the ​ ​ (a)   polynomial

• numerator
• denominator

Tags

CCSS.HSF-IF.C.7D

​ (a)   asymptotes may occur at the real zeros of the denominator

• Vertical
• Horizontal
• Slant

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CCSS.HSF-IF.C.7D

To determine if a graph has a horizontal asymptote, you compare the degree n of the numerator to the degree m of the denominator.

• y = 0

• n = m

• n < m

• No horizontal asymptote

• n > m

Tags

CCSS.HSF-IF.C.7D

Graphs can sometimes cross a horizontal asymptote.

• True

• False

Answer explanation

This is true.

Asymptotes apply to end behavior, therefore the graph may cross the horizontal asymptote when it is closer to zero.

Tags

CCSS.HSF-IF.C.7D

From the graph, we can see that the function has vertical asymptotes at

CHOOSE ALL THAT APPLY

• x = -3

• x = 1

• x = -1

• x = -2

• x = -4

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CCSS.HSF-IF.C.7D

• D = {x| x ≠ -4, 3, x ∈ R}

• D = {x| x ≠ 2, 3, x ∈ R}

• D = {x| x ≠ -4, 2, x ∈ R}

• D = {x| x ≠ 3, 4, x ∈ R}

• 3

• 1

• -1

• 2

• -4

Tags

CCSS.HSF-IF.C.7D

• 3

• 1

• -1

• 2

• -4

Tags

CCSS.HSF-IF.C.7D