Question

the graph of f(x), shown below in pink, has the same shape as the graph of g(x)=x^3, shown in gray. which of the following is the equation for f(x)?

Answer 1

Easily you can try each formula with x=-2

because we know f(-2)=-1

So ,in this way D is correct Only!!

Answer 2

D) f(x) = (x + 2)³ -1.

Explanation:

Given : the graph of f(x), shown below in pink, has the same shape as the graph of g(x)=x^3, shown in gray.

To find : which of the following is the equation for f(x).

Solution : We have given

Graph of f(x) is pink and graph of g(x) is gray.

We can see graph of f(x) is shifted to 2 unit left and 1 unit down

Because gray is at (0 ,0 ) and pink is at ( -2,-1)

By the transformation rule f(x) →→ f(x+h) -k.

It shows that graph is shifted to left by h unit and shifted down by k unit.

Then the equation of pink graph is :

f(x) = (x + 2)³ -1.

Therefore,D) f(x) = (x + 2)³ -1.