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Answer:

[tex](-\infty,+\infty)[/tex]

Step-by-step explanation:

The given function is

[tex]y=\sqrt[3]{x+8}[/tex]

The range refers to the values of y for which  x is defined.

We solve for x to obtain;

[tex]y^3=x+8[/tex]

[tex]x=y^3-8[/tex]

This is a polynomial function in y.

x is defined for all values of y.

Therefore the range is all real numbers.

or

[tex](-\infty,+\infty)[/tex]

The first choice is correct.

Answer:

range is -∞<y<∞

Step-by-step explanation:

[tex]y=\sqrt[3]{x+8}[/tex]

Range of the given function is same as the domain of the inverse function

LEts find the inverse for the given equation

Swap the variables x and y . then solve for y

[tex]y=\sqrt[3]{x+8}[/tex]

[tex]x=\sqrt[3]{y+8}[/tex]

Take cube on both sides

[tex]x^3= y+8[/tex]

Subtract 8 from both sides

[tex]y=x^3-8[/tex]

Inverse function is a cubic function. For cubic function the domain is set of allr eal numbers. -∞<x<∞

Range of the given function is same as the domain of the inverse function

So range is -∞<y<∞

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