# Transformations02

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Published on February 25, 2009

Author: heviatar

Source: slideshare.net

Stretches ... and some reflections. Ballet stretch

Translations y = ƒ(x - a) + b The role of parameter a: Examples a > 0 the graph shifts right a units. - the x-coordinates are increased a units. a < 0 the graph shifts left a units. - the x-coordinates are decreased a units. WARNING: watch the sign of a The role of parameter b: b > 0 the graph shifts up b units. - the y-coordinates are increased b units. b < 0 the graph shifts down b units. - the y-coordinates are decreased b units.

Stretches ... (and a wee bit about reflections) Let's start with a circle ... Let's look at some graphs ... We'll head over to fooplot.com ...

Stretches and Compressions: DICTIONARY 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 .

Find two equations for this graph, one in sine, the other in cosine.

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