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)

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

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

• Vertical
• Horizontal
• Slant

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

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.

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

• 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

• 3

• 1

• -1

• 2

• -4