Problem

Which one. is the graph of $f(x)=x^{3}$ ? What is its range?

Which one is the graph of $?(x)=x^{3} ?$ Choose the correct graph below.
A.
E.
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F.
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G.
D.
H.

Answer

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Answer

The range of $f(x)=x^{3}$ is all real numbers, \(\boxed{(-\infty, \infty)}\).

Steps

Step 1 :The function $f(x)=x^{3}$ is a cubic function. The graph of a cubic function is a curve that increases or decreases without any local maximum or minimum.

Step 2 :The range of a cubic function is all real numbers because there is no limit to how large or small the output can be when the input is a real number.

Step 3 :To identify the correct graph, we need to look for a curve that has no local maximum or minimum and passes through the origin (0,0) because $f(0)=0^{3}=0$.

Step 4 :The graph of $f(x)=x^{3}$ is a curve that increases or decreases without any local maximum or minimum and passes through the origin (0,0).

Step 5 :The range of $f(x)=x^{3}$ is all real numbers, \(\boxed{(-\infty, \infty)}\).

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