Question

Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.

The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).

Answer 1

The true statements are:
- The function has a domain of all real numbers.
- The function has a range of {y | −∞ < y < ∞} (all real numbers).
- The function is a reflection of y = ∛x (reflected across the x-axis).

Brief reasons: ∛x is defined for every real x and takes every real value, and f(x) = -∛x negates those values (so domain and range remain all reals and the graph is the x-axis reflection of y = ∛x). f is not increasing (it's decreasing), and f(3) = −∛3 ≈ −1.442, not −27.