Question

The function y=3/-x-3 is graphed only over the domain of{x|-8

Answer 1

Full Question:

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

Answer:

$-5 < y < -1$

Step-by-step explanation:

Given

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

Range: {x | –8 < x < 8}

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 $-5 < y < -1$