Rational Function Review

Identify the horizontal asymptote in the graph.

• y = 1/4

• y = 0

• none

• y = 4

Identify the vertical asymptote(s) in the graph.

• x = 1

• x = -3

• x = 2

• x = -4

• x = -2

Identify the y-intercept in the graph.

• (0, -1/3)

• (0, 1/4)

• (0, 3)

• (0, 4)

Find the oblique asymptote.

• y = 3x - 12

• y = x + 5

• y = 3x - 5

• y = 3x - 7

Which statement best describes the graph of \frac{x^2+9}{2x-6}?

• The graph has a vertical asymptote at x=3

• The graph has no vertical asymptote

• The graph has a vertical asymptote at x=-3

• The graph has vertical asymptotes at x=3 and x=-3

What is the equation of the graph pictured?

Mathematical Equivalence

ON

Label the graph

b

c

d

e

a

x-axis

origin

y-intercept

Vertical Asymptote

Horizontal Asymptote

• There is a hole at x=3

• There is a hole at x= -2

• The horizontal asymptote is at y=0

• The domain is {x|x≠2,3}

The horizontal asymptote equals zero when:

• the exponents in the numerator and denominator are equal

• the exponents in the denominator are greater than the numerator

• the exponents in the numerator are greater than the denominator

• the numerator equals zero

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• The function is discontinuous at x={-5, -3}