Rationals Discontinuity and Asymptotes

Determine the equations of any horizontal and vertical asymptotes and find any points of discontinuity (holes) of f\left(x\right)=\frac{x-3}{x^2-9}

Tags

MA.912.F.1.7

What's the horizontal asymptote of the function?

• y = 0

• No horizontal asymptote

• y = 1

• y = 9

Tags

CCSS.HSF-IF.C.7D

Find the vertical asymptote.

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

Tags

CCSS.HSF-IF.C.7D

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

Tags

CCSS.HSF-IF.C.7D

Identify any Vertical Asymptotes for this rational function

• There are none

• x = 2

• x = +/- 2

• x = 0, and x = - 2

Tags

CCSS.HSF-IF.C.7D

Identity any points of discontinuity (holes) in this rational function...

• hole at (-1/3, 1/3)

• no hole

• hole at (-1/3, 0)

• hole at (-1/3, -2)

Tags

CCSS.HSF-IF.C.7D

• x = 4

• y = 1/32

• y = 1.5

• y = 0

Tags

CCSS.HSF-IF.C.7D

Identify the x-value(s) of the hole(s) in the graph.

• There are no holes

Tags

CCSS.HSF-IF.C.7D

• 2

• -2

• -6

• 6

Tags

CCSS.HSF-IF.C.7D

Select ALL values that are excluded from the DOMAIN.

• x=1

• x=-1

• y=1

• x=0

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5