Pre-Cal 40S March 1, 2009
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The document discusses transformations of graphs including stretches, compressions, and translations. It provides examples of how the parameters a and b in the function y=f(x) affect whether the graph is stretched or compressed vertically or horizontally. It also prompts the reader to practice applying transformations to find coordinates of images of points and to determine the order of transformations in an equation.
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Pre-Cal 40S March 1, 2009
- 1. Looking Back At The Last Week I am looking forward, thinking back times by flickr user HAMED MASOUMI
- 2. FUNCTIONS FUNCTIONS odd even
- 3. Stretches and Compressions: The role of parameter a: Examples a > 1 the graph of ƒ(x) is stretched vertically. 0 < |a| < 1 the graph of ƒ(x) is compressed vertically. - the y-coordinates of ƒ are multiplied by a. The role of parameter b: b > 1 the graph of ƒ(x) is compressed horizontally. (Everything quot;speeds upquot;) 0<|b|<1 the graph of ƒ(x) is stretched horizontally. (Everything quot;slows downquot;) - the x-coordinates are multiplied by .
- 4. Putting it all together ... Try these examples ... y = ƒ(x) REMEMBER: stretches before translations Don't Look Behind Here Really! Are you sure you want to do this?
- 6. Practice what you've learned ... The coordinates of a point, A, on the graph of y = ƒ(x) are (-2, -3). What are the coordinates of it's image on each of the following graphs: The image of point B after each transformation shown above is given below as point C(n). Find the original coordinates of B. C3 (5, -4) C4 (-1, 6) C2 (-3, 7) C1 (2, 3) C5 (-4, -2)
- 7. Consider the equation below. Which transformation do you think should be applied first? second? third? fourth?