Transformations??

[TheKeyboardist]

I dont understand how to write and turn one transformation into another. For example:

Write the function for each graph described below:

The graph of f(x)=x^2 vertically stretched by a factor of 2 and translated one unit to the right.

I dont know how to write it out in numbers or write a numerical function into words. Can someone help me understand it or direct me to a site where this can be explained? Thanks.

By the way, nice new site layout.

 

[soroban]

Hello, TheKeyboardist!

The graph of \(\displaystyle f(x)\,=\,x^2\) vertically stretched by a factor of 2 and translated one unit to the right.

Given any function, \(\displaystyle f(x)\), there are a few simple rules.

\(\displaystyle a\cdot f(x)\): .The \(\displaystyle a\) is a vertical stretch/shrink factor.
. . If \(\displaystyle a\) is negative, the graph is reflected over the x-axis.

\(\displaystyle f(x\,-\,b):\) .The \(\displaystyle b\) is a horizontal translation.
. . The graph is moved \(\displaystyle b\) units to the right.

\(\displaystyle f(x)\,+\,c:\) .The \(\displaystyle c\) is a vertical translation.
. . The graph is moved up \(\displaystyle c\) units.


In your problem, \(\displaystyle f(x)\,=\,x^2\) is moved one unit to the right.
. . Replace \(\displaystyle x\) with \(\displaystyle x-1\), and we have: \(\displaystyle f(x)\,=\,(x\,-\,1)^2\)

It is vertically stretched by a factor of 2.
. . Append a coefficient of 2: .\(\displaystyle f(x)\,=\,2(x\,-\,1)^2\) . . . . there!

 

[TheKeyboardist]

thanks! What about horizontal compression and stretches?

How can you tell if something is vertical or horiziontally stretched or compressed?