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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

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

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ashishdwivedilVT

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

The given function is:

\(f(x)=2x\)

How horizontal reflection or reflection about the y-axis takes place?

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:

https://brainly.com/question/14323743

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