Question

The graph of f(x) = |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?

The range is the same for both functions: {y | y is a real number}.
The range is the same for both functions: {y | y > 0}.
The range changes from {y | y > 0} to {y | y > 2}.
The range changes from {y | y > 0} to {y | y > 6}.

Answer 1

Correct idea: f(x)=|x| has range {y | y ≥ 0}. After translating right 6 and up 2, new function is g(x)=|x−6|+2 with range {y | y ≥ 2}.

Among the given choices the intended one is the third (from >0 to >2), though strictly speaking the inequalities should be ≥, not >.