Question

Which statements describe the graph of y = 3√x-1+2 ? Check all that apply.

Answer 1

Answer: option A, D and E

Step-by-step explanation:

Answer 2

Answer:

The correct options are A, D and E.

Step-by-step explanation:

We are given the function $y=\sqrt[3]{x-1} +2$

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,

$y=\sqrt[3]{0-1} +2$

i.e. $y=-1+2$

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,

$0=\sqrt[3]{x-1} +2$

i.e. $-2=\sqrt[3]{x-1}$

i.e. $-8=x-1$

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).