Transcript More Fun With Functions

More Fun With Functions
September 28, 2010
Accelerated Math II
One Minute Question
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If f(x) = 3x - 2x2 + 7, find f(-1) + f(-2).
f(-1) = 3(-1) - 2(-1)2 + 7 = -3 -2 +7 = 2
f(-2) = 3(-2) -2(-2)2 +7 = -6 - 8 + 7 = -7
f(-1) + f(-2) = 2 - 7 = -5
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Is this equal to f(-3)???
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CONCLUSION!
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F(a+b)  F(a) + F(b)
This means that the value of a
function at a given number k isn’t
always equal to the sum of the values
of the function at two numbers just
because their sum is k.
Homework Problems??
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Would you like to have workbooks?
But look at adding functions!
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If f(x) = 2x + 1 and g(x) = -x + 2,
What should (f + g)(x) be???
Let’s check…
Operations of Functions
Find (f+g)(3)
 9+2+9=20
 Find (f-g)(x)
 -x2 + 3x + 2
 Find (f·g)(x)
 3x3 + 2x2
f
 Find  g  (5)
 
= 3  5  2 17
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2
25
5
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Suppose that
f(x) = 3x + 2
and
g(x) = x2
Applications
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The monthly cost of running a custom
sofa manufacturing company is:
C(x) = 3500 + 100x, where x is the
number of sofas made.
The revenue the company makes is
R(x) = 900x.
What is the profit function?
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Thirty people want to take a trip that
costs $1800 per person. The travel
agency decides to take $10 off each
fare for each additional person that
takes the trip. If x additional people
take the trip..
A) What is the total number of people
who take the trip?
B) What is each person’s fare as a
function of x?
C) What is the total amount the travel
agency takes in as a function of x?
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The cost of making a CD is a function of
the price of plastic. C(x) = 2.5x
The price of plastic is a function of the
rainfall in South America.
R(x) = -x2+3x+2
What is the cost of making a CD as a
function of the rainfall in South
America?
Compositions of Functions
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Suppose that
f(x) = 3x + 2
and
g(x) = x2
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Find f(2 +3)
8 + 33
Find g(x + 5)
x2 + 10x + 25
Find g(f(x))
g(3x + 2) = (3x + 2)2
9x2 + 12x + 4
Find f(g(2))
f(x2) = 3(22) + 2 = 14
Assignment:
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Page 114, 1-23 odd, 25 – 29
Page 115, 1-19 odd, 20
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Have fun!
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The Absolute Value Function
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This is
f(x) = |x|.
We call it
the
absolute
value
function.
The Greatest Integer Function
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This is
f(x) = [x].
We call it
the
greatest
integer
function.