Rational Functions and Their Graphs: Algebra 2 Math Quiz – PDF Download
Ten multiple-choice questions check your skill with rational functions: asymptotes, domain and range, holes, graph transformations of y = 1/x, and inverse variation. Choose the one correct answer, then read the explanation to learn the typical mistake.
Algebra 2Common Core: F-IF.C.7d · F-IF.B.4
🎯 Rational Functions and Their Graphs – Algebra 2 math quiz
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Question 1
What is the vertical asymptote of \(y=\frac{5}{x+7}-2\)?
A\(x=7\)
B\(x=-2\)
C\(x=2\)
D\(x=-7\)
Question 2
What is the horizontal asymptote of \(y=\frac{6x^{2}+1}{2x^{2}-5}\)?
A\(y=0\)
B\(y=6\)
C\(y=-\frac{1}{5}\)
D\(y=3\)
Question 3
Which equation matches the graph?A hyperbola with dashed asymptotes.
A\(y=\frac{2}{x+2}-1\)
B\(y=\frac{2}{x-2}-1\)
C\(y=\frac{2}{x-2}+1\)
D\(y=-\frac{2}{x-2}-1\)
Question 4
What is the domain of \(f(x)=\frac{x+3}{x^{2}-16}\)?
A\(x\neq 4\)
B\(x\neq -3\)
C\(x\neq 16\text{ and }x\neq -16\)
D\(x\neq 4\text{ and }x\neq -4\)
Question 5
How is the graph of \(y=\frac{1}{x-4}+3\) related to the graph of \(y=\frac{1}{x}\)?
ALeft 4 and up 3
BRight 4 and down 3
CRight 4 and up 3
DRight 3 and up 4
Question 6
The variable \(y\) varies inversely with \(x\), and \(y=6\) when \(x=4\). What is \(y\) when \(x=8\)?
A\(12\)
B\(48\)
C\(3\)
D\(24\)
Question 7
The table shows an inverse variation. What is the constant \(k\)?Values of an inverse variation.
A\(36\)
B\(20\)
C\(9\)
D\(18\)
Question 8
What is the range of \(y=\frac{1}{x+3}+4\)?
A\(y\neq -4\)
B\(y\neq 3\)
C\(y\neq 4\)
D\(y\neq -3\)
Question 9
The graph of \(f(x)=\frac{x^{2}-9}{x-3}\) is shown. What are the coordinates of the open circle?A line with one open circle.
A\((3,6)\)
B\((3,0)\)
C\((-3,0)\)
D\((6,3)\)
Question 10
A $240 bus rental is split equally among \(n\) students, so each pays \(c=\frac{240}{n}\) dollars. As \(n\) gets very large, what happens to \(c\)?
AIt becomes exactly $0
BIt gets close to $0 but never equals $0
CIt approaches $240
DIt grows without bound
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Remember:
Standards F-IF.C.7d and F-IF.B.4: graph rational functions and identify asymptotes, intercepts, domain and end behavior.
The graph of \(y=\frac{a}{x-h}+k\) has asymptotes \(x=h\) and \(y=k\) and center \((h,k)\).
A canceled factor \(x-c\) leaves a hole at \(x=c\); a factor that remains in the denominator gives a vertical asymptote.
Compare degrees: smaller numerator gives \(y=0\), equal degrees give the ratio of leading coefficients, larger numerator gives none.
Inverse variation \(y=\frac{k}{x}\) means the product \(xy\) is constant.
