Question

If the graph of the function f(x) = x2 is shifted 7units to the left, what is the equation of thetranslated graph?

Answer 1

STEP 1: Identify and Set Up

We have the function:

`f(x)=x^2`

Shifting the function to the left or right result in a horizontal shift and generally, it means we add or subtract the number of units when shifting left or right respectively. This will be shown in the next step.

STEP 2: Execute

We now implement the shift. We are moving 7 points to the left. This requires the addition of 7 to x based on our earlier established rule. Thus, we have:

`f(x)=(x+7)^2`