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

Answer 1

g(x) = ∛(x + 4), with domain x ≥ −4 (the third choice).

Check: g(−4)=∛0=0, g(0)=∛4≈1.587≈1.5, g(4)=∛8=2, which matches the graph.