Question

Use these parent functions.

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Which parent functions have a range of all real numbers? Select all that apply.
A. Linear
B. Quadratic
C. Absolute value
D. Exponential
E. Square root
F. Cube root

Answer 1

A and F.

- Linear (y = x) takes every real number as y, so its range is all real numbers.
- Cube root (y = ∛x) is defined for all real x and produces every real y (odd root), so its range is all real numbers.

The others have restricted ranges: quadratic, absolute value, and square root give y ≥ 0; exponential gives y > 0.