Graph of a function

[lewch45]

I need help with this problem....

Use the graph of F(x)=(x-1)^2/3 to sketch the graph of

a. y=-F(x)
B. y= F(-x)

I'm not even sure where to begin with this. Can anyone help?

 

[soroban]

Hello, lewch45!

Use the graph of \(\displaystyle F(x)\,=\.(x-1)^{\frac{2}{3}}\) to sketch the graph of

\(\displaystyle a)\;\;y\,=\,-F(x)\;\;\;\;\;\;b)\;\;y\,=\,F(-x)\)

First, they expect you to be able to graph: \(\displaystyle f(x)\,=\,(x-1)^{\frac{2}{3}}\)

          *     |                *
               *|           *
                |  *     *
                |    * *
      - - - - - + - - * - - - - 
                |     1

Then you should know that: \(\displaystyle y\,=\,-F(x)\) is reflected over the x-axis.
. . The graph is "flipped" vertically using the x-axis as the "pivot".

And you should know that: \(\displaystyle y\,=\,F(-x)\) is reflected over the y-axis.
. . The graph is "flipped" horizontally using the y-axis as the "pivot".

 

[lewch45]

Thanks....that makes sense.

 

[stapel]

Multi-post.