Answer:
The correct options are A, D and E.
Step-by-step explanation:
We are given the function [tex]y=\sqrt[3]{x-1} +2[/tex]
From the graph below, we see that,
Domain and range of the function is the set of all real numbers.
As y-intercept is the point where the graph of the function crosses y-axis.
That is, y-intercept is obtained when x= 0.
So, on substituting, we have,
[tex]y=\sqrt[3]{0-1} +2[/tex]
i.e. [tex]y=-1+2[/tex]
i.e. y= 1
Thus, the y-intercept is (0,1).
Also, x-intercept is the point where the graph of the function crosses x-axis.
That is, x-intercept is obtained when y= 0.
So, on substituting, we have,
[tex]0=\sqrt[3]{x-1} +2[/tex]
i.e. [tex]-2=\sqrt[3]{x-1}[/tex]
i.e. [tex]-8=x-1[/tex]
i.e. x= -7
Thus, the x-intercept is (-7,0).
Hence, the correct options for the function are,
A. The graph has a domain of all real numbers.
D. The graph has a y-intercept at (0, 1)
E. The graph has an x-intercept at (–7, 0).
