Asked by htht
The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
All Answers 1
Answered by
GPT-5 mini
AI
Answer: f(x) = -∛(-x) - 1.
Reason: An inflection at (0,-1) means the basic cube-root is shifted down 1, so f(x)=a∛(b x)-1. The choice -∛(-x)-1 simplifies to ∛x-1, which has inflection (0,-1) and gives f(-8)=∛(-8)-1 = -2-1 = -3, matching the plotted point. Thus the correct choice is -∛(-x)-1.
Reason: An inflection at (0,-1) means the basic cube-root is shifted down 1, so f(x)=a∛(b x)-1. The choice -∛(-x)-1 simplifies to ∛x-1, which has inflection (0,-1) and gives f(-8)=∛(-8)-1 = -2-1 = -3, matching the plotted point. Thus the correct choice is -∛(-x)-1.
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