Answer:
D) f(x) = (x + 2)³ -1.
Step-by-step 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.
