Question

Which statements describe the graph of y = Negative RootIndex 3 StartRoot x minus 1 EndRoot + 2? Select three options.

The graph has a domain of all real numbers.
The graph has a range of y greater-than-or-equal-to 1.
As x is increasing, y is decreasing.
The graph has a y-intercept at (0, 1).
The graph has an x-intercept at (–7, 0).

Answer 1

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:

Given: The graph is $y=\sqrt[3]{x-1}+2$

The domain of a function is a set of input values for which the function is real and defined.

Thus, the graph has a domain of $(-\infty, \infty)$.

To find the y-intercept:  To find the y-intercept, substitute $x=0$ in $y=\sqrt[3]{x-1}+2$.

$\begin{aligned}y &=\sqrt[3]{x-1}+2 \\&=\sqrt[3]{0-1}+2 \\&=-1+2 \\&=1\end{aligned}$

Thus, the y-intercept is $(0,1)$

To find the x-intercept: To find the x-intercept, substitute $y=0$ in $y=\sqrt[3]{x-1}+2$ .

$\begin{aligned}y &=\sqrt[3]{x-1}+2 \\0 &=\sqrt[3]{x-1}+2 \\-2 &=\sqrt[3]{x-1} \\(-2)^{3} &=(\sqrt[3]{x-1})^{3} \\-8 &=x-1 \\-7 &=x\end{aligned}$

Thus, the x-intercept is $(-7,0)$

Answer 2

Answer:

A. D. and E.

(this is for edg btw)