Asymptotes and Discontinuities

A line that the graph continually approaches but never touches is a(n) _____________________

• parabola
• asymptote
• rational function
• None of these

there is a vertical asymptote

• when the denominator equals zero
• when the degree of the numerator is exactly one more than the denominator
• when there is a common factor in the numerator and denominator
• when the degree of the numerator is the same as the denominator

There is a hole in the graph

• when the numerator and denominator have a common factor
• where the denominator equals zero
• if the degree of the numerator is exactly one more than the denominator
• if the degree of the numerator and denominator are the same.

You determine if the graph has a horizontal asymptote by

• setting the denominator equal to zero and solving
• comparing the degree of the numerator and denominator
• dividing the numerator and denominator
• determining if the numerator and denominator have a common factor.

State the vertical asymptote:

(x-2) / (x+5)

• x = -2/5

• x = -5/2

• x = -5

• x = 2

Find the Vertical Asymptotes. Hint: Factor (look for GCF)

• x= 0, -2

• x= 2

• x= -3, 2

• x = -3,1

Find the vertical asymptote(s).

• x = 3 and x = -7

• x = 3

• x = -7

• x = -4

Find the vertical asymptote(s). Hint: Factor

• x = 1 and x = -1

• x = 1

• x = -1

• x = 0

Find the horizontal asymptote.

(4x-16) / (x² - 16)

• y=2

• y=1

• y=0

• none

Find the horizontal asymptote.

• y = -2
• none
• y = 0
• y = 1/2