# Transformations of Functions

• Jun 12th 2007, 05:01 PM
SaRah<3
Transformations of Functions
I came on these questions that are confusing me so much, and I've been trying all day to figure it out. *so stressed*

This is the question:

Describe how the graph of each of the following functions can be obtained from the graph of y= f(x).
Where do I get the main points for y=f(x)....(like y=x(squared))????

and how do i graph y=-5f(x)+3, when there is two variables?

and the same is asked for this function:
y=1/3f(2x-6)-9

• Jun 12th 2007, 05:52 PM
Jonboy
Hmm I'll try to unstress. Let's let $f(x) = x^2$. This is the same as $y = x^2$

First graph $y = x^2$

So we have the modified version: $y= - 5f(x) + 3 \Rightarrow y = -5x^2 + 3$

Read over this first: Algebra (Math 1314) - Common Graphs - Transformations

So we have a reflection over the x - axis since the negative is outside paranthesis. Then a horizontal stretch be a factor of 5.

Also a vertical shift by a factor of 3.

So this means everytime you find a point for $y = x^2$ then you reflect it over the x - axis with a horizontal stretch w/a factor of 5 and move it up 3 units vertically.

Now for the next: $y = \frac{1}{3}f(2x-6) - 9$

This one is much tougher. Read through this and try:
Function Transformations / Translations: Basic Rules