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Transformation of Graphs
Literacy Research Memory Define each transformation. š š„ ā š šš„ , š š„+š , šš š„ , āš š„ , š āš„ , š š„ +š Sound waves are similar to sine and cosine graphs. If a sound created the function š(š„), find out what effect on the sound šš(š„) & š šš„ has. Find out how noise cancellation works in terms of transformations. Sketch the graphs of: š š„ = 1 š„ 2 š š„ = 1 š„ š š„ = š„ 2 š š„ = š„ 3 š š„ = š„ Key words: stretch, vector, scale factor, reflection, translation, parallel, axis You will need to know the shapes and any asymptotes of these graphs in order to transform them! Skills Practice Stretch Let š š„ = 1 š„ , sketch the graphs of: (i) š āš„ (ii)š š„ ā3 The graph š š„ = 1 š„ 2 has been translated by two places in the negative x direction. What is the new function? Give one example of a transformation that maps š š„ =š ššš„ to š š„ =ššš š„. ā š„ = š„ 2 . š š„ = š„ 2 +5š„ā3. Describe the transformation that maps ā š„ to š š„ 1. Describe how to sketch the graph of š¦=ā2š 2š„ +4. 2. Starting with a graph š¦=š(š„), if we shift it to the left by 3 and then stretch it horizontally by 2, what graph do we end up with? 3. With the same graph, what do we end up with if stretch horizontally by 2 first, then shift to the left by 3? 4. If š š„ = 1 š„ . What other transformation transforms š(š„) in the same way that āš(š„) does? 5. Let f(x) be shown in figure 3. Sketch the graphs and label the transformations of the coordinates from figure 3: 0.5š(š„) š( š„ 3 ) š(2š„+1)
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