1 Answer

Jgosmann · Answer 1 · 2021-09-23T21:49:13+0000

Full Question:

The function
$y =\sqrt[3]{-x} - 3$ is graphed only over the domain of –8 < x < 8. what is the range of the graph?

Answer:

-5 < y < -1

Explanation:

Given

Function:
$y =\sqrt[3]{-x} - 3$

Range: x

Required

Find the range of the graph

To calculate the range of the graph; we simply substitute the value of x (the domain) at both ends to the given function;

In other words, solve for y when x = -8 and when x = 8

To start with;

When x = -8

$y =\sqrt[3]{-x} - 3$

$y =\sqrt[3]{-(-8)} - 3}$

$y =\sqrt[3]{8} - 3}$

y =2 - 3

y = -1

When x = 8

$y =\sqrt[3]{-8} - 3$

y =-2 - 3

y = -5

Converting both values of y to inequalities

-5 < y < -1

Hence, the range of the graph is
-5 < y < -1

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