september 27 th
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Thursday, November 14 th. Warm-Up. Write a new equation g(x) compared to f(x) = 1/2x + 2 Shift up 7 Shift left 4. September 27 th. Homework Answers. What has changed?! . F(x). G(x). Part II-Transformations. Stretches & Compressions . - PowerPoint PPT PresentationTRANSCRIPT
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September 27th
Write a new equation g(x) compared to f(x) = 1/2x + 2
1. Shift up 7 2. Shift left 4
Warm-UpThursday, November 14th
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HOMEWORKANSWERS
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What has changed?!
G(x)F(x)
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Stretches &
Compressions
Part II-Transformations
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1. Stretches and compressions change the slope of a linear function.
2. If the line becomes steeper, the function has been stretched
vertically or compressedhorizontally.
3. If the line becomes flatter, the function has been compressed
vertically or stretched horizontally.
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Stretch vs. Compression
1.Stretches=pull away from y axis
2.Compression=pulled toward the y axis
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Horizontal vs. Vertical
1.Horizontal=x changes
2.Vertical=y changes
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Stretches and Compressions
Stretches and compressions are not congruent to the original
graph. They will have different rates of change!
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Use a table to perform a horizontal stretch of the function
y= f(x) by a factor of 3. Graph the function and the transformation on the same coordinate plane.
Step 2: Multiply each x-coordinate by 3.
Think: Horizontal(x changes) Stretch (away from y).
3x x y3(–1) = –3 –1 33(0) = 0 0 03(2) = 6 2 2
3(4) = 12 4 2
#1
Step 1: Make a table of x and y coordinates
Step 3: Graph
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Use a table to perform a vertical stretch of y = f(x) by a factor of 2. Graph the transformed function on the
same coordinate plane as the original figure.
Step 2: Multiply each y-coordinate by 2.
Think: vertical(y changes) Stretch (away from y).
#2
Step 1: Make a table of x and y coordinates
Step 3: Graph
x y 2y–1 3 2(3) = 60 0 2(0) = 0 2 2 2(2) = 44 2 2(2) = 4
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These don’t change!• y–intercepts in a horizontal stretch or compression• x–intercepts in a vertical stretch or compression
Helpful Hint
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Writing New Compressions
and Stretches
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.
#1
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# 2
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.
Let g(x) be a horizontal stretch of
f(x) = 6x -4 by a factor of 2 . Write the rule for g(x), and graph the function.
# 3