Rational Functions

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

• vertical

• horizontal

• slant

• none

This graph would have...

• An Oblique Asymptote

• HA @ y = 3

• HA @ y = 0

• No HA or OA

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}

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

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

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

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)

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

Give an example of an odd rational function with a numerator of 5x^3.

• f(x) = (-2x - x^2) / 5x^3

• f(x) = 5x^3 / (x^3 + 3x - 2)

• f(x) = 5x^3 / (3x^2 - x^3 + 7x)

• f(x) = 5x^2 / (x^2 - 3)

The graph shows the line y = -x + 8 and the curve f(x) = frac{3}{x-4} (A = 3). How many times does the line intersect the curve?

• 0

• 1

• 2

• 3