Full Question:
The function [tex]y =\sqrt[3]{-x} - 3[/tex] is graphed only over the domain of {x | –8 < x < 8}. what is the range of the graph?
Answer:
[tex]-5 < y < -1[/tex]
Step-by-step explanation:
Given
Function:[tex]y =\sqrt[3]{-x} - 3[/tex]
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
[tex]y =\sqrt[3]{-x} - 3[/tex]
[tex]y =\sqrt[3]{-(-8)} - 3}[/tex]
[tex]y =\sqrt[3]{8} - 3}[/tex]
[tex]y =2 - 3[/tex]
[tex]y = -1[/tex]
When x = 8
[tex]y =\sqrt[3]{-8} - 3[/tex]
[tex]y =-2 - 3[/tex]
[tex]y = -5[/tex]
Converting both values of y to inequalities
[tex]-5 < y < -1[/tex]
Hence, the range of the graph is [tex]-5 < y < -1[/tex]
