Question

Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?

a horizontal compression by a factor 2

a vertical stretch by a factor of 2

a horizontal translation 2 units to the left

a vertical translation 2 units down

Answer 1

Answer: A horizontal translation 2 units to the left

In this case, we are changing the variable x before it is being squared. This will have the effect of changing the input of the function. Imagine input 2 into the equation. Your first step would be to add 2. Therefore, you would need to start with a negative 2 to get us back to 0, or the beginning.

Since -2 is to the left of 0, the graph is moving 2 units to the left.