Unit 4 Review: Rational Functions

• x=-3

• x=-3 and x=8

• x=8

• x=-8

Answer explanation

Vertical asymptotes come from the denominator. Factor and cancel. Set the remaining denominator equal to 0 and solve.

Tags

CCSS.HSF-IF.C.7D

• y=0

• y=3

• y=1

• y=-3

Answer explanation

Compare the degree of the numerator and denominator to find the horizontal asymptote. When the degrees are equal divide the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

• y=x+8

• y=x-2

• y=x-8

• y=x+2

Answer explanation

There is a slant asymptote when the top degree is bigger than the bottom degree. Do polynomial long division to find the equation of the slant asymptote.

Tags

CCSS.HSF-IF.C.7D

• (0,-8)

• (0,8)

• (0,4)

• (0,2)

Answer explanation

A y-intercept occurs when x=0. Substitute 0 for x and simplify.

Tags

CCSS.HSF-IF.C.7D

• (16,0)

• (4,0)

• (-4,0)

• (4,0) & (-4,0)

Answer explanation

To find the x-intercepts, factor and cancel first. Then, set the remaining numerator equal to 0 and solve. There can be more than one x-intercept.

Tags

CCSS.HSF-IF.C.7D

• (6,0)

• (-6,-2)

Answer explanation

Holes occur where there is a factor in the numerator and denominator that cancel. To find the complete hole, set the canceled factor equal to 0 and solve for the x-coordinate. Then, substitute this value into the simplified function and simplify for the y-coordinate.

Tags

CCSS.HSF-IF.C.7D

What is the equation of the graph shown?

Answer explanation

It's usually a good idea to check the key features of the graph and equation. Check to see which ones have the same asymptotes and intercepts.

Tags

CCSS.HSF-IF.C.7D

Answer explanation

Use cross multiplication to solve when there is one fraction on each side of the equal sign.

Tags

CCSS.HSA.REI.A.2

Tags

CCSS.HSA.REI.A.2