Answer:
The correct options are A, D and E.
Step-by-step explanation:
We are given the function ![y=\sqrt[3]{x-1} +2](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx-1%7D%20%2B2)
From the graph below, we see that,
Domain and range of the function is the set of all real numbers.
<em>As y-intercept is the point where the graph of the function crosses y-axis.</em>
That is, y-intercept is obtained when x= 0.
So, on substituting, we have,
![y=\sqrt[3]{0-1} +2](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B0-1%7D%20%2B2)
i.e. 
i.e. y= 1
Thus, the y-intercept is (0,1).
<em>Also, x-intercept is the point where the graph of the function crosses x-axis.</em>
That is, x-intercept is obtained when y= 0.
So, on substituting, we have,
![0=\sqrt[3]{x-1} +2](https://tex.z-dn.net/?f=0%3D%5Csqrt%5B3%5D%7Bx-1%7D%20%2B2)
i.e. ![-2=\sqrt[3]{x-1}](https://tex.z-dn.net/?f=-2%3D%5Csqrt%5B3%5D%7Bx-1%7D)
i.e. 
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).