Question

Which statements describe the graph of y = Vx-1 + 2? Select three options.O The graph has a domain of all real numbers.O The graph has a range of y ≥ 1.O As x is increasing, y is decreasing.O The graph has a y-intercept at (0, 1).U The graph has an x-intercept at (-7, 0).

Answer 1

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)

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:

`\begin{gathered} y=\sqrt[3]{x-1}+2 \\ y=\sqrt[3]{0-1}+2 \\ y=-1+2 \\ y=1 \end{gathered}`

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:

`\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}`

Then, the x-intercept is the point (-7, 0)