How do we perform transformations of functions?

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Presentation transcript:

How do we perform transformations of functions? 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.

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

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

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

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

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

Sketch y = x2-1

Sketch y = x2-1

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

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

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

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

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

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

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

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

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

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