Question

The graph of f(x) = |x| is translated 6 Units to the right and two units up from a new function. Which statement about the range of both function is true?

Answer 1

DOMAIN: All Real Numbers OR (-∞,∞)

RANGE: y ≥ 2 or [2,∞)

Explanation:

The original function f(x) = |x| has a v-shape and the vertex (tip) is at (0,0).

The domain of f(x) = |x| is all real numbers. Shifting it to the right is not going to change the domain.

The range of f(x) = |x| is y ≥ 0 because the "V" opens upward and starts at zero. Moving the function up two units will move the vertex up by 2 so the function now starts at y=2 and goes up, so the range is y ≥ 2.