chapter 3: transformations of graphs and data
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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 - PowerPoint PPT PresentationTRANSCRIPT
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