Question

Which 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

Interpretation: y = -∛(x − 1) + 2.

True statements:
- The graph has a domain of all real numbers. (∛ is defined for all real x.)
- As x is increasing, y is decreasing. (∛(x−1) is increasing; the leading negative flips it to decreasing.)

False statements (with why):
- The graph has a range of y ≥ 1. — False. ∛(x−1) takes all real values, so -∛(x−1)+2 also takes all real values (range = all real numbers).
- The graph has a y-intercept at (0, 1). — False. At x=0: y = -∛(-1)+2 = 1+2 = 3, so y-intercept is (0, 3).
- The graph has an x-intercept at (–7, 0). — False. Set y=0: ∛(x−1)=2 → x−1=8 → x=9, so x-intercept is (9, 0).

Note: Only two of the given five statements are correct (the prompt asking for three is likely an error).