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U2 Rational Functions Test Q3

This document contains a multi-part math test on rational functions with 6 questions. It includes questions that ask students to: 1) Graph a rational function, labeling asymptotes and stating the domain and range. 2) Simplify and evaluate radical and rational expressions. 3) Simplify rational variable expressions, stating any restrictions. 4) Write the equation of a rational function that has been transformed by horizontal and vertical stretching. 5) Find the perimeter and restrictions of a rectangle given its dimensions. 6) Find the width of a rectangle given its area and length expressions.

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Farhan Habibzai
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168 views4 pages

U2 Rational Functions Test Q3

This document contains a multi-part math test on rational functions with 6 questions. It includes questions that ask students to: 1) Graph a rational function, labeling asymptotes and stating the domain and range. 2) Simplify and evaluate radical and rational expressions. 3) Simplify rational variable expressions, stating any restrictions. 4) Write the equation of a rational function that has been transformed by horizontal and vertical stretching. 5) Find the perimeter and restrictions of a rectangle given its dimensions. 6) Find the width of a rectangle given its area and length expressions.

Uploaded by

Farhan Habibzai
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Name: ________________________ Date: __________________

______ ______ TI: _______ COMM: _______ Unit 2 Test


20 K 11 A LEVEL LEVEL Rational Functions
Version A
KNOWLEDGE: All work must be shown for full marks.
1. Graph the following rational function. Show any necessary work to earn full marks.
Label the asymptotes on the graph. Then, state the domain and range.

2
𝑓(𝑥) = −3
1
− 𝑥+1
2
[4 K]

[2 K]
Domain: ________________________ Range: ________________________

2. Rewrite each expression in radical form first, where necessary. Then, evaluate each expression.

𝟒 b)
𝟖 −
a) ( )
𝟑 (3𝑘𝑚2 )−3 (2𝑘 −2 𝑚3 )−1
𝟏𝟐𝟓
[4 K]

[2 K]
3. Simplify the following rational variable expressions. State all restrictions:

𝑥+5 𝑥+2
a) +
𝑥+1 𝑥−2
[4 K]

𝑥 2 +2𝑥−15 𝑥−6
b) ×
𝑥 2 −9𝑥+18 𝑥+5
[4 K]

APPLICATION: All work must be shown for full marks.

4. The graph of y  f (x) where f (x ) is a rational function is vertically stretched by a factor of 2,


horizontally stretched by a factor of 3.
The function has a horizontal asymptote of 1 and a vertical asymptote of -1.
Write the equation of the transformed rational function.

[2 A]
5. Given the following rectangle:

a) Find the simplified perimeter of the rectangle.


7𝑥 + 2 b) State ALL restrictions [5 A]
𝑥

4𝑥 2 + 3𝑥 − 8
𝑥2

𝑥 2 −7𝑥+10 𝑥 2 −2𝑥
6. If the area of the rectangle below is and the length is find its width, w.
𝑥+2 𝑥 2 +5𝑥+6
[4 A]
Thinking: All work must be shown for full marks.
3
Create a rational expression that has the restrictions 2, and − and which simplifies to the
4
𝑥+4
expression . Justify your work and state all restrictions.
4𝑥+3

Your final answer should show the numerator and denominator in standard form.

[Level]

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