Question

hich statements describe the graph of y = Negative RootIndex 3 StartRoot x minus 1 EndRoot + 2? Select three options.

The graph has a domain of all real numbers.
The graph has a range of y greater-than-or-equal-to 1.
As x is increasing, y is decreasing.
The graph has a y-intercept at (0, 1).
The graph has an x-intercept at (–7, 0).

Answer 1

y = -∛(x − 1) + 2.

True:
- The graph has a domain of all real numbers. (Cube root is defined for all real x.)
- As x is increasing, y is decreasing. (∛(x−1) is increasing, multiplying by −1 makes it decreasing.)

False:
- The graph has a range of y ≥ 1. False — because ∛(x−1) takes all real values, so y = -∛(x−1)+2 also takes all real values (range: all real numbers).
- The graph has a y-intercept at (0, 1). False — y(0) = -∛(−1)+2 = -(-1)+2 = 3, so the y-intercept is (0,3).
- The graph has an x-intercept at (−7, 0). False — solve 0 = -∛(x−1)+2 → ∛(x−1)=2 → x=9, so the x-intercept is (9,0).

Note: only two of the given statements are correct.