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Thread: Transformations of Functions

  1. #1
    Jun 2006

    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:

    Thank-you very much in advance!
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  2. #2
    Member Jonboy's Avatar
    May 2007
    South Point
    Hmm I'll try to unstress. Let's let $\displaystyle f(x) = x^2$. This is the same as $\displaystyle y = x^2$

    First graph $\displaystyle y = x^2$

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

    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 $\displaystyle y = x^2$ 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: $\displaystyle y = \frac{1}{3}f(2x-6) - 9$

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