Rational Functions

• 4x - 2

• 4x + 2

• 4x - 2 + (1/3x - 1)

• 4x + 2 + (1/3x - 1)

When finding the Horizontal asymptotes of a function, you should be thinking...

• Set Bottom = to Zero

• Top = 0

• f(0)

• Look at the Degree of the top and bottom...

Which asymptote(s) are determined by looking at the denominator?

• vertical

• horizontal

• slant

• none

Graph

• A

• B

• C

• D

Find the horizontal or oblique asymptote.

• y = x

• y = x - 8

• y = x - 4

• y = x + 4

This graph would have...

• An Oblique Asymptote

• HA @ y = 3

• HA @ y = 0

• No HA or OA

State the equation of the rational function that this graph represents.

• y = -2x + 1 / x - 3

• y = 2x + 1 / x - 3

• y = -2x + 1 / x+ 3

• y = 2x + 1 / x + 3

State the range of f(x) = 1 / 3x + 4.

• {y ∈ R | y > -4/3}

• {y ∈ R | y ≠ -4/3}

• {y ∈ R | y > 0}

• {y ∈ R | y ≠ 0}

The graph of which of the following rational functions has a hole?

• y = 2x - 6 / x - 6

• y = 2x - 3 / x - 3

• y = 2x - 6 / 2x

• y = 2x - 6 / x - 3

Identify the vertical and horizontal asymptotes of f(x) = x - 4 / 2x + 1.

• vertical: x = 4, horizontal: y = -1/2

• vertical: x = 4, horizontal: y = 1/2

• vertical: x = -1/2, horizontal: y = 1/2

• vertical: x = 1/2, horizontal: y = -1/2