Rational Functions

Give the domain of f(x) = (2(x-2)^2) / ((x-2)(x+5)).

• {x | x ≠ 2, -5, x ∈ ℝ}

• {x | x ≠ -2, 2, -5, x ∈ ℝ}

• {x | x ≠ -2, 2, 5, -5, x ∈ ℝ}

• {x ∈ ℝ}

For what value of A, will the function f(x) = frac{A}{x-4} intersect the line y = -x + 8 exactly once?

• A = 4

• A = 8

• A = 12

• A = 16

Tags

CCSS.HSA.REI.A.2

Which is the (practical) example of a rational function with a discontinuity?

• f(x) = (2x^2 + 8) / (x^2 + 1)

• f(x) = (2x + 4) / (x^2 + 2)

• f(x) = 2x - 4

• f(x) = (2x^2) / (x + 2)

• f(x) = 1 / (x^2 + 4)

Tags

CCSS.HSF-IF.C.7D

Which is an example of a reciprocal function.

• f(x) = (2x^2 + 8) / (x^2 + 1)

• f(x) = (2x + 4) / (x^2 + 2)

• f(x) = 2x - 4

• f(x) = (2x^2) / (x + 2)

• f(x) = 1 / (x^2 + 4)

Tags

CCSS.HSF-IF.C.7D

• y = -2

• y = 0

• y = 1/2

• x = 2

• none

Tags

CCSS.HSF-IF.C.7D

Label the graph

b

c

d

e

a

y-intercept

x-axis

Horizontal Asymptote

Vertical Asymptote

origin

Tags

CCSS.HSF-IF.C.7D

What is the equation of the graph pictured?

Mathematical Equivalence

ON

Tags

CCSS.HSF-IF.C.7D

Give the equation(s) of all asymptotes for f(x) = (2(x-2)^2) / ((x-2)(x+5)).

• x = 2

• x = -5

• x = 2, y = 2

• x = 2, x = -5, y = 2

• x = -5, y = 2

Tags

CCSS.HSF-IF.C.7D

Which of the following have an oblique asymptote?

• f(x) = 3x / (x-2)

• f(x) = (x^2 - 4x + 5) / (3x - 2)

• f(x) = -2 / (4 - 3x)

• f(x) = (-2x) / ((x-1)(x+1))

• f(x) = (3x^2 - 4x + 2) / x

Tags

CCSS.HSF-IF.C.7D

Give the equation of the oblique asymptote for rational function frac(3x^2-4x+2)/x

• y = 0

• y = 3

• y = 3x - 4

• y = 1/3x - 4

• y = 3x + 1

Tags

CCSS.HSF-IF.C.7D