CHAPTER
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-1 Changing Windows
Homework: Lesson Master 3-1 plus Section 3-1 problems #13, 17, 19, 20
New Terms:
1. Transformation
2. Viewing Window
3. Default Window
4. Asymptote
5. Points of Discontinuity
6. Parent Functions (show all)
[pic]
7. List the criteria of a sketch:
Activity:
1. Give a viewing window for f(x) = 12+ 4x – ½ x2 that shows all the key features of the parabola.
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-2 The Graph Translation Theorem
Homework: pp. p. 170 #6-17
New Terms:
1. Translation image
2. Preimage
Definitions:
Translation:
Theorems:
The Graph-Translation Theorem: The relation described by the sentence x and y, the following processes yield the same graph:
1.
2.
Teacher Examples:
1. Under the translation, the image of (0,0) is (7,8).
a. Find a rule for this translation.
b. Find the image of (6,-10) under this translation.
2. a. Compare the graphs of y=x3 and y+5=(x+4.2)3
b. Find the coordinates of a point on each graph.
3. If the graph of y=x2 is translated 2 units up and 3 units left, what is the equation for its image.
4. Prove that every translation is a distance preserving transformation.
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-3 Translations of Data
Homework: p.176 4,5,7-12
New Terms:
1. Translation of a set of data
Proofs:
Prove that under a translation of h, the MEAN of the image set of data is h units more than the mean of the original data set.
Activity:
1. Refer to Example 1. Compute the deviations from the mean for the original set of data and for the image set. What do you notice?
Theorems:
1.
2.
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-4 Symmetries of Graphs
Homework: 3-4 p.183 #1,7,8-10,13
New Terms:
1. Symmetry with respect to the y axis
2. Symmetry with respect to the x axis
3. Symmetry with respect to the origin
4. Even Function
5. Odd Function
Teacher Examples:
1. Prove that the squaring function is an even function.
2. Prove y=x + x3+2x5 is symmetric to the origin.
3. Use the calculator to show that f(x) = 2x3 is even, odd, or neither.
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-5 The Graph Scale Change Theorem
Homework: 3-5 p.191#7-12
New Terms:
1. Vertical Scale Change
2. Horizontal Scale Change
3. Graph Scale Change Theorem
4. Negative Scale Factors
Teacher Examples: The line 41x – 29y = 700 contains the points (39, 31) and (10, -10). Use this information to obtain two points on the line with equation 20.5x – 87y = 700.
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-6 Scale Changes of Data
Homework: 3-6 p.198 #4-9,11,12
New Terms:
1. Scale change
2. Scale factor
3. Scale image
4. Scaling or rescaling
Proof p.196 (Under a scale change of “a”, the mean of the data set is a times the original mean)
Theorems:
1. (Mean Median Mode)
2. (Variance Standard Deviation Range)
Teacher Examples:
1. The teachers in a school have a mean salary of $30,000 with a standard deviation of 4,000. If each teacher is given a 5% raise, what will be their new mean salary and what will be their new standard deviation.
2. To give an approximate conversion from miles to kilometers you can multiply the number of miles by 1.61. Suppose the data are collected about the number of miles that cars can go on a tank of gas. What will be the effect of changing from miles to kilometers on:
a. The median of the data?
b. The variance of the data?
c. The standard deviation of the data?
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-7 Composition of Functions
Homework: p.205 #5-16
New Terms:
1. Composite
2. Commutative
3. Domain of a Composite
Copy Examples 2 and 3:
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Teacher Examples:
1. Let f(x)= x2 and g(x)=[pic]. Evaluate:
a. f(g(4))
b. g(f(4))
c. [pic]
2. Find formulas for f(g(x)) and g(f(x)).
3. Verify that [pic]
4. Give the domain of f, g and [pic]
CHAPTER 3 Transformations of Graphs and Data
SECTION 3-8 Inverse Functions
Homework: p.212 #2-13,15
New Terms:
1. Inverse of a function
2. Horizontal Line Test for Inverses
3. Give Example of how the Horizontal line test is used: (p.209)
|Function f |Pass? |Inverse |Function? |
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4. Inverse Function Theorem
Teacher Examples:
1. Find the inverse of S={(1,1,), (2,4), (3,9), 4,16)}
2. Find an equation for the inverse and tell whether the inverse is a function. Verify your answers by taking composites.
a. f(x)=6x+5
b. y=[pic]
3. Are f(x)=m2 and g(x)=m-2 inverses? Justify your answer.
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