1. Compositions Notes
Add earlier graphs where they have to say what is f(3)…
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2. Function Compositions
Lecture: 2D Pre AP & GT Precalculus

3. Homework page 64 #88
Corners of equal size are cut from a square with sides of length 8 meters
A. Write the area of the figure as a function of
Area Function:
Book Domain: (0,4) … Alternative
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4. Homework page 64 #88 B. Book Range: (32,64) Alternative (0,64)
Sometimes there are multiple interpretations of an authentic problem. Problems can have multiple solutions
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5. Homework page 64 #88 C. If the figure has no area
If x=4, the figure is a square with side
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6. Agenda
Combining Functions
Function Compositions
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7. Function Algebra
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8. Example
Given find such that: a. a: b. b: c. c:
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9. Composition We say, “f composed with g of x” OR “f of g of x”
Range of g(x) is the domain of f(g(x))
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10. Examples
If and then
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11. Graphical Example
Based on the function to right, what is
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12. Example
If and then
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13. Composition Graphically
The point a is in the domain
The red line is the range of f(x) but is also the domain of g(f(x))
On a graph to change from domain to range shift left to y=x to find corresponding domain element of g(x)
Then find corresponding point in the range of g(x) and hence the range of g(f(x)).
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14. Reflection Is for all functions, f and g? Counterexample:
No, this is not true…composition is not commutative, order matters.
Counterexample:
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15. Fractal Curves are made via a function composition process
Show & Tell
Fractal Curves are made via a function composition process
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16. Composition CalisthenicsF G
F o G
Match across the columns
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17. Homework
Pg 89 #6-12(even) Pg 90 #44-50 (even)
Pg 91 #62
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