Question

The graph below has the same shape as the graph of G(X) = x2, but it isshifted down four units and to the left three units. Complete its equation.Enter exponents using the caret (1); for example, enter x2 as x^2. Do notinclude "F(x) =" in your answer.

Answer 1

To move a function up, you add outside the function: f (x) + b is f (x) moved up b units.

Moving the function down works the same way; f (x) – b is f (x) moved down b units.

To shift a function left, add inside the function's argument: f (x + b) gives f (x)shifted b units to the left. Shifting to the right works the same way; f (x – b) is f (x) shifted units to the right.

Given that

`G(x)=x^2`

If this function is shifted down four units and to the left three then we will have

`f(x)=(x+3)^2-4`

Therefore, you will write

(x+3)^2-4