The graph of [tex]\rm f(x) = \sqrt[3]{x} - 4[/tex] is attached below and this can be sketched by substituting the values of x in the function f(x) and then plotting the points on the graph.
Given :
[tex]\rm f(x) = \sqrt[3]{x} - 4[/tex]
The following steps can be used in order to determine the graph of the given function f(x):
Step 1 - Determine the value of f(x) at the values of x = {-8,-4,0,4,8}.
Step 2 - At (x = -8) the value of f(x) is given by:
[tex]\rm f(x) = \sqrt[3]{-8} - 4[/tex]
[tex]\rm f(x) = -2 - 4 = -6[/tex]
Step 3 - At (x = -4) the value of f(x) is given by:
[tex]\rm f(x) = \sqrt[3]{-4} - 4[/tex]
f(x) = -5.6
Step 4 - At (x = 0) the value of f(x) is given by:
[tex]\rm f(x) = \sqrt[3]{0} - 4[/tex]
f(x) = -4
Step 5 - At (x = 4) the value of f(x) is given by:
[tex]\rm f(x) = \sqrt[3]{4} - 4[/tex]
f(x) = -2.4
Step 6 - At (x = 8) the value of f(x) is given by:
[tex]\rm f(x) = \sqrt[3]{8} - 4[/tex]
f(x) = -2
Step 7 - Now, plot the points obtained in the above steps on the graph in order to draw the graph of the given function [tex]\rm f(x) = \sqrt[3]{x} - 4[/tex]
The of the function [tex]\rm f(x) = \sqrt[3]{x} - 4[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/4700926
