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)?

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carlosego carlosego · Answer 1 · 2018-10-16T21:25:51+02:00

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 [tex]y = f (-x)[/tex], the graph of [tex]y = f (x)[/tex] is reflected on the y-axis. (Horizontal reflection)

If [tex]f (x) = 2x[/tex], to obtain g (x) as a horizontal reflection, we evaluate

[tex]g (x) = f (-x)[/tex]

Thus:

[tex]g (x) = f (-x) = 2 (-x)g (x) = - 2x[/tex]

Answer:

[tex]g (x) = - 2x[/tex]

See attached image

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-26T08:30:59+02:00

The graph that represents the reflection of f(x)=2x is g(x)=-2x.

The given function is:

[tex]f(x)=2x[/tex]

If graph of a function f(x) is reflected about y-axis, f(x) becomes f(-x).

So, g(x) = f(-x)

Given f(x) =2x

So, f(-x) =-2x

So, g(x) =-2x

So, the required function is g(x) =-2x which is a straight line with a negative slope passing through the origin.

Thus, the graph that represents the reflection of f(x)=2x is g(x)=-2x.

To get more about graphs visit:

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