Answer
The graph has a domain of all real numbers
The graph has a y-intercept at (0, 1)
The graph has an x-intercept at (-7, 0)
Step-by-step explanation
In a cubic function, the domain and range are all real numbers
In a cubic function, as x is increasing, y is also increasing.
To find the y-intercept of the graph, we need to substitute x = 0 into the formula of the function, and find the y-value, as follows:
[tex]\begin{gathered} y=\sqrt[3]{x-1}+2 \\ y=\sqrt[3]{0-1}+2 \\ y=-1+2 \\ y=1 \end{gathered}[/tex]Then, the y-intercept is the point (0, 1)
To find the x-intercept of the graph, we need to substitute y = 0 into the formula of the function, and find the x-value, as follows:
[tex]\begin{gathered} y=\sqrt[3]{x-1}+2 \\ 0=\sqrt[3]{x-1}+2 \\ 0-2=\sqrt[3]{x-1} \\ (-2)^3=x-1 \\ -8+1=x \\ -7=x \end{gathered}[/tex]Then, the x-intercept is the point (-7, 0)