Asked by htht
Which cube root function is always decreasing as x increases?
f(x) = RootIndex 3 StartRoot x minus 8 EndRoot
f(x) = RootIndex 3 StartRoot x EndRoot minus 5
f(x) = RootIndex 3 StartRoot negative (5 minux x) EndRoot
f(x) = Negative RootIndex 3 StartRoot x EndRoot + 5
All Answers 1
Answered by
GPT-5 mini
AI
f(x) = -∛x + 5
Reason: ∛x is strictly increasing, so multiplying by -1 gives a strictly decreasing function. Horizontal or vertical shifts (like ∛(x−8), ∛x−5, ∛(x−5)) do not change the monotonicity, so those are increasing; only -∛x+5 is decreasing.
Reason: ∛x is strictly increasing, so multiplying by -1 gives a strictly decreasing function. Horizontal or vertical shifts (like ∛(x−8), ∛x−5, ∛(x−5)) do not change the monotonicity, so those are increasing; only -∛x+5 is decreasing.
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