Combinations of Functions

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Combinations of Functions
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Warm Up Graph the piecewise function.
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Operations with Functions

• Sum
• Difference
• Product
• Quotient

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Example Let f(x) 5x² -2x 3 and g(x) 4x²
7x -5

• Find f g

• Find f - g

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Example
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Using your GDC
Start with VARS
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Example Let f(x) 5x² and and g(x) 3x 1.

• Find f g

• Find f/g

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Example
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Example f(x)2x 3 and g(x) x -7
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Lets take a look graphically.
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Find

4
5
1
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Find
- 4
0
- 4
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Find
0 -
4
- 4
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Find
3 -
(- 4)
7
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Find
5 x
4
20
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Find
- 3 x
5
- 15
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Find
6
3
2
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Composition of Functions
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• A composite function is a combination of two
  functions.
• You apply one function to the result of another.

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• The composition of the function f with the
  function g is written as f(g(x)), which is read
  as f of g of x.
• It is also known as which is read
  as f composed with g of x.
• In other words

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Ex f(x)2x 5 and g(x) x - 3

• You can work out a single rule for the
  composite function in terms of x.

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• Do you think will give you
  the same result?

NO!
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You Try.
f(x) 2x 2
g(x) (x 2)2

• Find

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You may need to evaluate a composite function for
a particular value of x.
Method 1 Work out the composite function. Then
substitute 3 for x.
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You may need to evaluate a composite function for
a particular value of x.
Method 2 Substitute 3 into g(x). Substitute
that value into f(x).
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• Now, lets take a look at it graphically

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Find
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Find
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Find
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Find
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Find