Question

The function f(x) = x^2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)^2?

Answer 1

We are given the following parent function f(x)

`f(x)=x^2`

The transformed function g(x) is

`g(x)=(x+1)^2`

Notice that the change is done in the horizontal direction.

Recall that the transformation rule for the horizontal translation to the left is given by

`f(x)\rightarrow f(x+c)`

Where c is the number of units by which the graph is shifted to the left.

So, we should expect that the graph is horizontally shifted to the left by 1 unit.

Therefore, the above is graph represents the transformed function g(x) which is horizontally shifted to the left by 1 unit.