Question

Identify the parent function for the function g(x) = (x + 1)3 based on its function rule.

Then graph g and identify the transformation of the parent function that it
represents.
O cubic; translation up 1 unit
O cubic; translation left 1 unit
cubic; translation right 1 unit
O quadratic; translation down 1 unit

Answer 1

Cubic; translation up 1 unit

Answer 2

cubic; translation left 1 unit

Explanation:

The parent function of g(x) = (x + 1)3 is f(x) = x3. Therefore, the function is cubic.

Graph both functions on a graphing calculator.

The cubic parent function f(x) = x3 intersects the x-axis at the point (0, 0).

The function g(x) = (x + 1)3 intersects the x-axis at the point (−1, 0).

Because (−1, 0) is 1 unit left of (0, 0), the function g(x) = (x + 1)3 represents a horizontal translation of the parent function 1 unit left.