Question

The graph of f(x) = 2x. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?

Answer 1

Reflect across y axis means that you replace x with -x

f(-x)=2(-x)=-2x
g(x)=-2x
de graph is the one that passes through (0,0) and (1,-2) and -1,2)

Answer 2

For this case we have transformation of functions:

Reflection is the mirror image of a figure. It can also be defined as the turning of points and graphs around the axes.

So, we have:

To graph $y = f (-x)$, the graph of $y = f (x)$ is reflected on the y-axis. (Horizontal reflection)

If $f (x) = 2x$, to obtain g (x) as a horizontal reflection, we evaluate

$g (x) = f (-x)$

Thus:

$g (x) = f (-x) = 2 (-x)g (x) = - 2x$

Answer:

$g (x) = - 2x$

See attached image