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Standards: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition. How do we perform transformations of functions?

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In your own words, describe what a parent function is.

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Function What the graph will look like. Name y = x linear y = ×2 quadratic y = x3 Cubic y = lxl absolute value y = -x y = -×2 y = -x3 y = -lxl rational y = 1/x y = 2x y = -(2x) exponential square root

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Shifting Graphs: aka Translations Suppose c>0 y=f(x)+c→shifts f(x) c units up y=f(x)- c→shifts f(x) c units down y=f(x-c) →shifts f(x) c units right y=f(x+c)→shifts f(x) c units left

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Stretching Graphs: aka Dilations Suppose c>1 y=cf(x) →stretches f(x) vertically by a factor of c. This means the graph is narrower y = f(x)/c →compresses f(x) vertically by a factor of c. This means the graph is wider y = f(cx) →compresses f(x) horizontally by a factor of c. This means the graph is narrower y=f(x/c) →stretches f(x) horizontally by a factor of c. This means the graph is wider

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Reflecting Graphs: aka Reflections y=-f(x) →reflects f(x) about the x-axis y=f(-x) →reflects f(x) about the y-axis

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Sketch y = x2-1

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Now Sketch y=|x2-1|

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Sketch y = x2-1 Now Sketch y=|x2-1|

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Given f(x) the graph, Perform the transformation to create f(x - 2) + 3.

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Given f(x) the graph, Perform the transformation to create - f(x).

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Given f(x) the graph, Perform the transformation to create f(-x).

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Given f(x) the graph, Perform the transformation to create f(x + 2) - 3.

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Given f(x) the graph, Perform the transformation to create - f(x - 5).

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Given f(x) the graph, Perform the transformation to create - (f(x - 4) + 1).

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Which of the following graphs is the graph of the function ? 1. 2. 3. 1 A B C

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Homework P. 48 # 1-8 Graph each function and describe the transformations.

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