Name:_______________________
Date assigned:______________
Band:________
Precalculus | Packer Collegiate Institute
Rational Functions #1
Warm Up: Multiplying Functions Together! Togethes!!!
We are graphically going to multiply two functions together.
f ( x)  2 and g ( x )  x .
Let h( x)  f ( x) g ( x) .
To get us primed, find h(2)  ______ and h(3)  ______
Now do this for all the points! And for all the glory!!!
f ( x)
g ( x)
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h( x )  f ( x ) g ( x )
Section 1: Graphically Multiplying Functions Together
Do the same. Multiply the first two functions graphed to find the product of those functions. Do not do it algebraically.
Problem 1:
Problem 2:
2
Problem 3:
Problem 4:
3
Problem 5:
Problem 6:
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Section 2: Dividing Functions
Dividing two functions is slightly harder to do graphically. Remember that order matters for division!
Try it! First, find h(3)  ____, h(2)  ____, h(1)  ____, h(0)  ____, h(1)  ____, h(2)  ____, h(3)  ____
f ( x)
g ( x)
h( x )  f ( x ) / g ( x )
f ( x)
g ( x)
h( x )  f ( x ) / g ( x )
Problem 1:
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Problem 2:
f ( x)
g ( x)
h( x )  f ( x ) / g ( x )
f ( x)
g ( x)
h( x )  f ( x ) / g ( x )
Problem 3:1
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Careful! Remember the Greatest Sin of Mathematics! Thou shalt not divide by….
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Problem 4:
f ( x)
h( x )  f ( x ) / g ( x )
g ( x)
I’d like for you to check your final graph by filling in this very special table of values…
 f ( x)  ________________
 g ( x)  ________________
In order to do that: 
x
-3
-2
-1
0
0.5
0.9
0.99
1
1.01
1.1
1.5
2
f ( x)
g ( x)
h( x )
If you need to modify your graph based on the table of values, please do so.
Follow Up! When we divide functions, we see crazy/unexpected things happen when… [continue this sentence, and
explain why the crazy things happen]…
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3
Problem 5: Challenge!
f ( x)
g ( x)
h( x )  f ( x ) / g ( x )
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Section 3: Observations
Multiplying Functions
1. When multiplying functions, when one part of a function doesn’t exist (e.g. a hole, a chunk of the function is
missing), what happens to the product function at those values?
2. When multiplying functions, when one function has an x-intercept (and the other function exists), what is true
about the product function?
3. When multiplying functions, when one function has a constant height of 1, how does that affect the product
function?
Dividing Functions
4. When dividing functions, we have a problem with dividing by zero. When the denominator of a function is zero,
what possible things can happen in the quotient function at those values?
5. When dividing functions, when is the quotient function going to hit the x-axis? How do you know?
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