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?