chapter 3: transformations of graphs and data

Do Now:

• Using your calculator, graph y = 2x on the following windows and sketch each below on page 1 of the Unit 2 Lesson 3-1 Lesson Guide:

10 1010 10

xy

50 5010 10

xy

5 510 10xy

Chapter 3: Transformations of Graphs and Data

Lesson 1: Changing Windows

Mrs. Parziale

Vocabulary

• Transformation: is a one-to-one correspondence between sets of points.– Two types of transformations:

• Translations• Scale Changes

• Asymptote: a line that the graph of a function approaches and gets very close to, but never touches.

• Parent function: the general form of a function, from which other related functions are derived.

Set Notation Reminder

• Use the following notation when describing domains and ranges of various functions.

is read "the set of all x, such that x is an element of the real numbers and x is greater than 0."

is read "the set of all y, such that y is an element of the real numbers and y is greater than -5 and less than +5."

, 0x x x

, 5 5y y y

Example 1:

• Using your calculator, graph y = 2x on the following windows and sketch each below:

10 1010 10

xy

50 5010 10

xy

5 510 10xy

Example 1:

10 1010 10

xy

50 5010 10

xy

5 510 10xy

• Using your calculator, graph y = 2x on the following windows and sketch each below:

Common Parent Functions

• Name: ______________ • Domain: __________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? _________________

none

Linear

none

Graph y x

{ : Real Numbers}x x{ : Real Numbers}y y

Name: Quadratic Function

• Domain: ____________• Range: ______________

• Asymptotes? __________ • Points of discontinuity? _________________

none

none

2Graph y x

{ : 0}y y

{ : Real Numbers}x x

Name: Cubic Function

• Domain: ____________• Range: ______________

• Asymptotes? _________• Points of discontinuity? _________________

none

none

3Graph y x

{ : Real Numbers}x x

{ : Real Numbers}y y

Name: Square Root function

• Domain: ____________• Range: ______________

• Asymptotes? _________• Points of discontinuity? _________________

none

none

Graph y x{ : 0}x x

{ : 0}y y

Name: Absolute Value Function

• Domain: ______________• Range: ______________

• Asymptotes? __________• Points of discontinuity? _________________

none

none

Graph y x

{ : 0}y y

{ : Real Numbers}x x

Name: Exponential Function

f(x) = bx (b>1)

• Domain: ______________• Range: ______________

• Asymptotes? _________• Points of discontinuity? _________________none

y = 0

xGraph y b

{ : Real Numbers}x x{ : 0}y y

Name: Inverse Function

• Domain: ______________ • Range: ______________

• Asymptotes? _________• Points of discontinuity? _________________ Hyperbola

x = 0 , y = 0

x = 0

1Graph yx

{ : Real Numbers, 0}x x x

{ : Real Numbers, 0}y y y

Name: Inverse Square Function

• Domain: ______________ • Range: ______________

• Asymptotes? _________• Points of discontinuity? _________________

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Inverse Square 2

1( )f xx

x = 0 , y = 0

x = 0

2

1Graph yx

{ : 0}y y { : Real Numbers, 0}x x x

Name: Greatest Integer Function

• Domain: ______________ • Range: ______________ • Asymptotes? __________ • Points of discontinuity? __________________________

none

Integral values of x

Graph y x

{ : Real Numbers}x x{ : Integral Numbers}y y

What you should show on a graph

An acceptable graph shows:• Axes are labeled• Scales on the axes are shown• Characteristic shape can be

seen• Intercepts are shown• Points of discontinuity are

shown• Name of function is included

Closure

• What graphs are these?

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y