Question

The graph shows the function g(x) for a restricted domain.

On a coordinate plane, a function starts at (negative 4, 0) and then curves through the y-axis at (0, 1.5) and then goes through point (4, 2).

Which is the function g(x) for a restricted domain?


g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4
g(x) = Negative RootIndex 3 StartRoot x EndRoot minus 4; x greater-than-or-equal-to 0
A or B

Answer 1

Check the values:

- For A, g(x) = −∛(x+4). g(−4) = 0 (ok), but g(0) = −∛4 ≈ −1.587 (does not match 1.5).
- For B, g(x) = −∛x − 4. g(0) = −4 and g(4) = −∛4 − 4 ≈ −5.587 (both do not match).

So as written, neither A nor B matches the plotted points. The correct function that fits the points (−4,0), (0,≈1.587≈1.5), (4,2) is

g(x) = ∛(x + 4), x ≥ −4.

If you must pick one of the two given choices and assume a sign typo, pick A (interpreting it without the leading negative).