Reflections and Dilations of Absolute Value Functions — Quiz
Question 1 • Mathematics II
Which absolute value function, when graphed, represents the parent function, f of x is equal to absolute value of x , reflected over the x -axis and translated 1 unit to the right?
Answer
A
f of x is equal to negative start absolute value x minus 1 end absolute value
B
f of x is equal to start absolute value negative x minus 1 end absolute value
C
f of x is equal to absolute value of negative x plus 1
D
f of x is equal to negative absolute value of x plus 1
Explanation
Reflecting the parent function f(x) = |x| over the x-axis changes it to f(x) = -|x|. Translating that graph 1 unit to the right replaces x inside the absolute value with x - 1, giving f(x) = -|x - 1|. This is choice A. Choice D, -|x| + 1, shifts the graph up instead of right.
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