Unit 4: Functions, Relations, and Transformations

Unit 4: Functions, Relations, and Transformations

Unit Objectives.

• Interpret graphs of functions and relations• Review function notation.• Learn about the linear quadratic, square root,

absolute-value families of functions.• Apply transformation-translation, reflection,

and dilations to the graphs of functions.• Transform functions to model real-world data.

November 7, 2014

• Objectives:1. Interpret graphs of real-world functions.2. Identify the maximum and minimum of

graphs.3. Given a real-world situation make a graphical

interpretation.

Sketch a graph that shows the relationship of time as the independent variable to the height of the fluid in the beaker as the dependent variable. Show your work on the white board. a. b. c.

November 13, 2014

Objectives:

1. Students will define a function in terms of the relationship between the independent and dependent variables.

2. Students will apply function notation and review the vertical line test.

3. Define the domain and range of a function.

What is a function?

Function definition

Function: A relationship for which every value for the independent (x) variable has at most one value of the dependent (y) variable.

Function f is defined by the equation and function g is defined by the graph below:

3 4

2

xf x

x

November 14, 2014Objectives:1. Explore what happens to the equation of a

line when you translate the line.2. Learn how to write an equation that

translates a function horizontally h units and vertically k units.

3. Describe the graph of an equation in the form by relating it to the graph of .

( )y f x h k ( )y f x

Warm-Up

On your calculator graph the following:

2

( )

( )

( )

( )

f x x

f x x

f x x

f x x

Warm-Up

On your calculator graph the following:

2

( )

( )

( )

( )

f x x

f x x

f x x

f x x

The graph of the line is translated right 4 units and down 5 units. Write an equation of the new line.

How does the graph of compare with the graph of

1

3y x

( 3)y f x ( )?y f x

• November 17, 2014

• Objectives:1. Examine the graph of 2. Find equations for translation of the graph

Warm-up: Problems A, B on handout.

2y x

2y x

November 18, 2014

Objectives:1. Introduce the Square Root function and perform transformation: up, down, right, left. 2. Perform reflection of a function across the y and x axis.

y x

November 20, 2014

Objectives:1. Students will analyze how graphs are

reflected across the y-axis and x-axis.2. Practice problems from units 1-4.

Dec. 1 2014, Warm-Up

Use the formula for the partial sum of geometric series: to find the sum of

3 + 6 + 12 + 24 + …. + 1536, where

1(1 )

1

n

n

U rS

r

1 3U

Objectives

• Understand how to apply dilation to a function (vertical and horizontal stretch)

Dilation Scale factor Stretch

Rigid transformation

Non-rigid transformation

December 2, 2014

Objectives:1. Describe two ways to tell if a graph is a rigid

transformation of a parent function.2. Apply the rules for the dilation of a function.

Warm-Up problems 1 – 4.

1.

2.

3.

4.

December 3, 2014

Objectives:1. More on Dilation of functions

• Page 226, problems 2, 3

• Page 227, problem 7

December 10, 2014

• Objectives: Students will brainstorm the big ideas of the first semester units.1. Recursive Sequence.2. Linear Systems3. Statistics4. Transformation of Functions.

• Each table will be assigned one of the first semester units.

• Your table will be given 10 minutes to write down as much information about that unit.

Such as: big ideas, terms, examples ect.

Remember you are up against at least one other table. Let’s see who does a better job.