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The function y = RootIndex 3 StartRoot x EndRoot – 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?

{y | –5 < y < 5}
{y | –5 < y < –1}
{y | 1 < y < 5}
{y | 1 < y < –1}

Respuesta :

Edufirst

Answer:

  • {y | –5 < y < - 1}

Explanation:

The graphed function is:

  • [tex]y=\sqrt[3]{x}-3[/tex]

And it is graphed over the domain {x | –8 < x < 8}, which is all the real numbers greater than - 8 and less than 8.

The cube root is a continuous growing function over all the real numbers.

Thus, to find the range you can just substitute the border numbers, -8 and 8, into the function, to find the corresponding y-values.

For x = - 8:

  • [tex]y = \sqrt[3]{-8}-3=-\sqrt[3]{8}-3=-2-3=-5[/tex]

For x = 8

  • [tex]y=\sqrt[3]{8}-3=\sqrt[3]{8}-3=2-3=-1[/tex]

Hence, the range is {y | –5 < y < -1} ← answer

Answer:

B

Step-by-step explanation:

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