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Back to Tutor Intake Assessment: Graph rational functions

HSF.IF.C.7.d Tutor Intake -- Rational Function Key Features

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Grade 9·10 problems·~12 min·Common Core Math - HS Functions·standard·hsf-if-c-7d
Work through problems with immediate feedback
A

Concepts

1

For f(x)=(x−2)(x+3)(x−2)(x−5)f(x) = \dfrac{(x-2)(x+3)}{(x-2)(x-5)}, what happens at x=2x = 2?

2

Which rule correctly determines the horizontal asymptote of a rational
function p(x)q(x)\dfrac{p(x)}{q(x)} when deg⁡(p)=deg⁡(q)\deg(p) = \deg(q)?

3

For h(x)=x3+1x2−4h(x) = \dfrac{x^3 + 1}{x^2 - 4}, how many horizontal asymptotes
does the graph have? Enter 0 or 1.

B

Procedures

1

For f(x)=x2−9x2−x−6f(x) = \dfrac{x^2 - 9}{x^2 - x - 6}, identify all x-intercepts
(zeros). Select the correct list.

2

Find the x-coordinate of the hole in the graph of
g(x)=x2−4x−2g(x) = \dfrac{x^2 - 4}{x - 2}.
Enter the x-value only.

3

For f(x)=3x−6x2−3x−10f(x) = \dfrac{3x - 6}{x^2 - 3x - 10}, find all vertical
asymptotes. Enter the larger x-value of the two vertical asymptotes.

4

Determine the horizontal asymptote of
f(x)=4x2−12x2+3xf(x) = \dfrac{4x^2 - 1}{2x^2 + 3x}.
Enter the y-value of the horizontal asymptote as a fraction or decimal.
(Example: enter 22 for y=2y = 2.)

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