Transformations of Functions: Algebra 2 Math Quiz – PDF Download
Ten multiple-choice questions check your skill with transformations of functions: shifts, reflections, stretches, even and odd symmetry, and the graphs of square root, cube root and exponential functions. Choose the one correct answer, then read the explanation.
Algebra 2Common Core: F-BF.B.3 · F-IF.C.7b
🎯 Transformations of Functions – Algebra 2 math quiz
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Question 1
How is the graph of \(y=(x-3)^{2}\) related to the graph of \(y=x^{2}\)?
AShifted left 3
BShifted up 3
CShifted down 3
DShifted right 3
Question 2
Which describes the graph of \(g(x)=|x+4|-2\) compared with \(y=|x|\)?
ALeft 4 and down 2
BRight 4 and down 2
CLeft 4 and up 2
DLeft 2 and down 4
Question 3
Which equation matches the parabola?A parabola with vertex (2, -1).
A\(y=2(x+2)^{2}-1\)
B\(y=\frac{1}{2}(x-2)^{2}-1\)
C\(y=2(x-2)^{2}-1\)
D\(y=2(x-2)^{2}+1\)
Question 4
Is \(f(x)=x^{3}-x\) even, odd or neither?
AEven
BOdd
CNeither
DBoth even and odd
Question 5
What is the domain of \(y=\sqrt{x-6}+1\)?
A\(x\ge 1\)
B\(x\le 6\)
C\(x\ge 6\)
D\(x\ge -6\)
Question 6
Which equation matches the cube root graph?A cube root curve with center (-2, 1).
A\(y=\sqrt[3]{x-2}+1\)
B\(y=\sqrt[3]{x+2}+1\)
C\(y=\sqrt[3]{x+2}-1\)
D\(y=\sqrt[3]{x-1}+2\)
Question 7
The point \((4,-6)\) is on the graph of \(y=f(x)\). Which point is on the graph of \(y=f(2x)\)?
A\((8,-6)\)
B\((4,-12)\)
C\((2,-3)\)
D\((2,-6)\)
Question 8
Which function is the graph of \(y=\sqrt{x}\) reflected over the y-axis?
A\(y=-\sqrt{x}\)
B\(y=\sqrt{-x}\)
C\(y=-\sqrt{-x}\)
D\(y=\sqrt{x-1}\)
Question 9
The graph of \(y=2^{x}-3\) is shown. What is its horizontal asymptote?An exponential graph.
A\(y=-3\)
B\(y=3\)
C\(y=0\)
D\(y=-2\)
Question 10
Which expression equals \(2^{x+3}\)?
A\(6\cdot 2^{x}\)
B\(2^{x}+3\)
C\(8\cdot 2^{x}\)
D\(3\cdot 2^{x}\)
🎉 Quiz complete!
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Remember:
Standards F-BF.B.3 and F-IF.C.7b: identify the effect of transformations and graph square root, cube root and other basic functions.
\(f(x)+k\) shifts vertically; \(f(x+k)\) shifts horizontally in the opposite direction of the sign.
\(a\cdot f(x)\) stretches or compresses vertically; \(f(kx)\) compresses or stretches horizontally by \(\frac{1}{|k|}\); a negative factor reflects.
Even: \(f(-x)=f(x)\). Odd: \(f(-x)=-f(x)\). Test by substituting \(-x\).
\(y=\sqrt{x-h}+k\) starts at \((h,k)\); \(y=\sqrt[3]{x-h}+k\) is centered at \((h,k)\).
