identify the graph as a translation of a basic function, and write the formula for the graph. basic…

Explanation:

Step1: Identify the basic function

The basic cubic function is (y = x^{3}).

Step2: Determine the horizontal translation

The graph of (y=x^{3}) is shifted (3) units to the left. For a function (y = f(x)), a horizontal shift (h) units to the left is given by (y=f(x + h)). Here (h = 3), so we replace (x) with (x+ 3) in the basic function.

Answer:

Basic function: (y=x^{3}) Formula for the graph: (y=(x + 3)^{3})