7
QuizMultiple Choice

Absolute Value Functions and Translations — Quiz

Question 7 • Mathematics II

Which functions have a vertex with an x -value of 0 ? Choose three correct answers.

Answer
A
f of x is equal to absolute value of x
B
f of x is equal to absolute value of x minus 6
C
f of x is equal to absolute value of x plus 3
D
f of x is equal to start absolute value x plus 3 end absolute value minus 6
E
f of x is equal to start absolute value x plus 3 end absolute value

Explanation

A vertical shift changes a graph’s height but not the x-coordinate of its vertex. In A, |x| has its vertex at x = 0; in B, |x| − 6 and in C, |x| + 3, the changes are vertical shifts, so their vertices still have x = 0. In D and E, the x is shifted inside the absolute value, making the vertex’s x-coordinate −3.

AI-written and checked against the verified answer.

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