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?

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

FunctionWhat the graph will

look like.Name

y = xlinear

y = ×2

quadratic

y = x3 Cubic

y = lxlabsolute value

y = -x

y = -×2

y = -x3

y = -lxl

rationaly = 1/x

y = 2xy = -(2x)

exponential

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 Sketchy=|x2-1|

Sketch y = x2-1

Now Sketchy=|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.

2.

3.

1

A

B

C

Homework P. 48 # 1-8

Graph each function and describe the transformations.