Question

Write the equation for the following function that represents a horizontal shift left 4 and avertical shrink by a factor of 2 on the parent function f (x) = x²?

Answer 1

We are given the parent function f(x) = x^2.

We are tasked to find an equation for that function that represents a 4-unit horizontal shift to the left and a vertical shrink by a factor of 2.

First, let u shift the function horizontally. This means adjusting f(x) = x^2 to f(x) = (x - h)^2, where h is equal to the horizontal movement. Because we are moving the function 4 units to the left, then h = -4. So, the new function become f(x) = (x -(-4))^2 or f(x) = (x + 4)^2.

Next, let's shrink the function by a factor of 2. This means that the original y-values are halved. So f(x) = (x + 4)^2 must be transformed to f(x) = 1/2 (x + 4)^2.

The new equation is f(x) = 1/2 (x + 4)^2.