Question

Given the function f(x)=x^2 and g(x)=(-x)^2-1 what transformations will occur if both functions are graphed on the same coordinate grid?

Answer 1

We are given the following two functions

`\begin{gathered} f(x)=x^2 \\ g(x)=(-x)^2-1 \end{gathered}`

Recall that the rule for reflection over the y-axis is given by

`f(x)\rightarrow f(-x)`

As you can see, the graph of g(x) will be a reflection over the y-axis of the graph f(x).

Recall that the rule for vertical translation (upward) is given by

`f(x)\rightarrow f(x)-d`

The above translation will shift the graph vertically upward by d units.

For the given case, d = 1

As you can see, the graph of g(x) will be a vertical translation of the graph f(x)

Therefore, we can conclude that the graph of g(x) will be a reflection over the y-axis and a vertical translation of the graph f(x).

1st option is the correct answer.