10
QuizMultiple Choice

Absolute Value Functions and Translations — Quiz

Question 10 • Mathematics II

The graph of f of x is equal to absolute value of x is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

Answer
A
The range is the same for both functions: start set y such that y is greater than or equal to 0 end set .
B
The range is the same for both functions: start set y such that y is a real number end set .
C
The range changes from start set y such that y is greater than or equal to 0 end set to start set y such that y is greater than or equal to 6 end set .
D
The range changes from start set y such that y is greater than or equal to 0 end set to start set y such that y is greater than or equal to 2 end set .

Explanation

The graph of f(x) = |x| has its lowest point at (0, 0), so its range is y ≥ 0. Translating it 6 units right moves the lowest point horizontally but does not change its height; translating it 2 units up moves the lowest point to y = 2. Thus, the range changes to y ≥ 2, as stated in choice D.

AI-written and checked against the verified answer.