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Unit Test 7a: Rational Functions
By Teerani Sutthiphansakul
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Last updated about 3 years ago
17 questions
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Question 1
1.
Simplify \frac{8n}{n-3}+\frac{3n}{5n-6}
\frac{43n^{2}-9}{(5n-6)(n-3)}
\frac{8n+5n}{(n-3)+(5n-6)}
\frac{11n}{6n-9}
\frac{43n^{2}-57n}{(n-3)(5n-6)}
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Question 2
2.
Subtract \frac{8}{x^{2}-x-2}-\frac{3}{x^{2}-4}
\frac{5x+1}{(x-2)(x+2)(x+1)}
\frac{5x+13}{(x-2)(x+2)(x+1)}
\frac{11x+19}{(x-2)(x+2)(x+1)}
\frac{5x+19}{(x-2)(x+2)(x+1)}
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Question 3
3.
Simplify: \frac{1}{n+5}\cdot\frac{n^{2}+2n-15}{n-8}
\frac{n-3}{(n+5)(n-8)}
\frac{n^{2}+2n-14}{2n-3}
\frac{n-3}{n-8}
\frac{n^{2}+2n-15}{(n+5)(n-8)}
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Question 4
4.
Solve for x: \frac{1}{x-8}+\frac{1}{x^{2}+x-72}=\frac{6}{x-8}
-\frac{44}{5}
-22
22
\frac{44}{5}
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Question 5
5.
Solve for x:\frac{x}{2x-3}=\frac{3x}{x+11}
x={1,3}
x={0,4}
x={-4,0}
x={5,2}
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Question 6
6.
Given the function f(x)=-\frac{2}{x-3}+5, identify the horizontal asymptote.. You do not need to show work for this one.
y=5
y=3
x=5
x=3
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Question 7
7.
Graph f(x)=\frac{2}{x-1}-3. Label the asymptotes and two orded pairs on each branch.
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Question 8
8.
Simplify \frac{m^{2}+m-30}{m^{2}+13m+42}\div\frac{m-2}{m+7}
\frac{m^{2}+2n-32}{m^{2}+14m+49}
\frac{-5}{2m^2}
\frac{m-5}{m-2}
\frac{(m-5)(n-2)}{(m-7)^2}
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Question 9
9.
Forf(x)=\frac{-2x^2-2x}{x^2-3x-4} , what is the equation of the horizontal asymptote
There isn't one
y=0
y=-2
y=2
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Question 10
10.
For f(x)=\frac{2x(x+1)}{(x-3)(x+1)}
​
, what are the coordinates of the holes, if it\they exist.
(-1,\frac{1}{2})
(-1,-2)
there isn't one
(-1,-\frac{1}{2})
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Question 11
11.
For f(x)=\frac{2x(x+1)}{x^2-3x-4}
, what is the equation of the vertical asymptote
x=0
x=4
x=-1, x=4
x=-1
Question 12
12.
For f(x)=\frac{2x^{2}+2x}{x^2-2x-3}what is the Domain
x\neq\{3\}
x\neq\{3,-1\}
x\neq\{-1\}
x\neq\{3,1\}
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Question 13
13.
Find the x-intercept, if one exists: f(x)=\frac{x^{2}+2x}{x^{2}+x}...
I see that the option isn't here.. you will all get credit for this one....
(1,0),(-1,0)
(2,0)
(0,0)(1,0)
(-2,0)
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Question 14
14.
What is the equation of the rational function graphed below:
\frac{1}{x-2}
\frac{1}{x+2}
\frac{x}{x-2}
\frac{x^{2}}{x-2}
\frac{x}{x+2}
\frac{x^{2}}{x+2}
Question 15
15.
What is the equation of the vertical asymptote? f(x)=\frac{4x^{2}+8x}{x+3}
x=3
x=-3
x=0
x=-2
Question 16
16.
Which statements are true for the given rational function. Select all that apply.
f(x)=\frac{x^{2}-6x}{x^2-4x-12}
The horizontal asymptote is at y=0.
There is a hole at (6,\frac{3}{4})
The vertical asymptote is at x=-2.
The
x
and
y
intercepts are at the origin.
The domain is all real numbers except -2.
Question 17
17.
Write an equation for the graph below:
\frac{x^{2}+x-2}{x+2}
\frac{x^{2}+x-2}{x-1}
\frac{1}{x-1}
\frac{x^{2}}{x^{2}-1}