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M3-020-A12-V03
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F-BF.4.a
Warmup
M3-020-A12-V03
Find inverse functions for simple invertible functions, including rational examples.
Reflect inverse points and graph features across y=x
Problem
Reflect the horizontal asymptote \(y~=~0\) across \(y~=~x\). State the inverse asymptote and explain how a positive original range becomes the inverse domain.
Answer choices
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A
Rule: swap x and y across y=x. Original feature: horizontal asymptote y=0. Inverse feature: horizontal asymptote labeled x=0. The feature type is not changed from horizontal to vertical.
B
Rule: leave x and y unchanged. Original feature: horizontal asymptote y=0. Inverse feature: horizontal asymptote y=0. The positive original range remains an output range rather than becoming the inverse domain.
C
Rule: swap x and y across y=x. Original feature: horizontal asymptote y=0. Inverse feature: vertical asymptote x=0. The positive original range becomes inverse domain x>0.
D
Rule: reflect across the x-axis by negating y. Original feature: horizontal asymptote y=0. Inverse feature: horizontal asymptote y=0. The positive original range is incorrectly changed to inverse domain x<0.
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Curriculum context
Standard F-BF.4.a
Category Functions
Domain Building Functions
Objective Find inverse functions for simple invertible functions, including rational examples.
Problem type Reflect inverse points and graph features across y=x
