Question

What transformation is made from f(x) → f(-x)?

Answer 1

Answer:

A) reflection across the y-axis

Step-by-step explanation:

If $f(x)=f(-x)$, then this says that two $y$-coordinates are equal for opposite values of $x$.

Let $(a,b)$ a point on $f$.

Then $f(a)=b$.

We also know that $f(-a)=b$ and therefore $(-a,b)$ is also a point on the graph.

If you graph [/tex](-a,b)[/tex] and $(a,b)$ you will see they are symmetrical to each about the $y$-axis.

Example if given both $f(x)=f(-x)$ and $f(2)=3$, then $f(-2)=3$. This means both (2,3) and (-2,3) are points on the graph.

Here is what those two points look like on a Cartesian Plane (please see graph in picture).