Asymptotes and Discontinuities

Which of the following is determined by just looking at the denominator?

• vertical asymptote

• horizontal asymptote

• holes

• slant asymptote

Find the vertical asymptote.
g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

• 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

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on

• there is something left in the denominator

• the value of f(0)

• a factor in the denominator cancels with a factor in the numerator

• 2

• -2

• -6

• 6

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

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

• x=0

• x=-3

• x=6

• x=-7

• x=3

What are the asymptotes?

• x=-2 and y=-1

• x=-2 and y=1

• x=2 and y=1

• x=2 and y = -1

Find the Vertical Asymptotes

• x= 0, -2

• x= 2

• x= -3, 2

• x = -3,1

What are the Vertical Asymptotes of...

• x = 0, -5

• x=0, 5

• x = 2, -7

• x = -2, 7