20
QuizMultiple Choice

Absolute Value Functions and Translations — Quiz

Question 20 • Algebraic Reasoning

Which graph represents the function f of x is equal to start absolute value x plus 3 end absolute value ?

Answer
A
Image with description On a coordinate plane, an absolute value graph has a vertex at (3, 0).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 3).
C
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).

Explanation

The graph of y = |x| has its vertex at (0, 0). In f(x) = |x + 3|, adding 3 inside the absolute value shifts the graph 3 units left, so the vertex is at (−3, 0). Therefore, the correct choice is the graph with a vertex at (negative 3, 0).

AI-written and checked against the verified answer.

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