Question

Which of the following graphs corresponds to the function above

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=\sqrt[3]{x-2}$

we know that

The parent function of f(x) is equal to g(x)

$g(x)=\sqrt[3]{x}$

The rule of the transformation of g(x) to f(x) is equal to

(x,y)------> (x+2,y)

That means------> The translation is 2 units to the right

Using a graphing tool

The graph in the attached figure

Answer 2

Answer with explanation:

We are given a function f(x) as:

                      $f(x)=\sqrt[3]{x-2}$

We know that the function intersects the x-axis when x=2

Since when x=2 we have:

  $f(x)=\sqrt[3]{2-2}=\sqrt[3]{0}=0$

Hence, the graph of the function passes through the point (2,0).

Also, when x<2 then x-2<0

and hence the function will take negative value.

i.e. f(x)<0 when  x<2

and when x>2 the f(x)>0

Hence, the graph of the function is attached to the answer.