Question

The graph of the function g(x) is a transformation of the parent functionf(x) = x^2?Which equation describes the function g?

Answer 1

Let's begin by listing out the information given to us:

The parent function f(x) is defined by the expression: f(x) = x^2

We will observe that the function g(x) shifts 3 units to the left.

The standard form is given by:

(x - h)²

This implies that g(x) moves from (0, 0) to (-3, 0)

⇒ h = -3 & vertex x= -3

Substituting the value of "h" into the standard form expression, we have:

(x - - 3)² ⇒ (x + 3)²

⇒ g(x) = (x + 3)²

g(x) = (x + 3)²