1. 4.2 Notes.notebook February 19, 2013
4.2 Combining Functions Algebraically
Now that we have seen the graphs of combined functions,
and realize that when we add 2 functions the result is the sum
of their y values, we can realize that this result is the sum as
ALGEBRAICALLY combining their equations to produce a new
equation.
This new equation will automatically give the same value as the
sum of the 2 original equations. This process also works for the
other 3 operations.
Ex) Put f(x) = 3x­8 and g(x) = ­2x+5 into your calculator.
Graph them and also graph (f+g)(x).
Test the values you get for x=1
f(1)= ______ g(1) = _______ (f+g)(1) = ______
Now ALGEBRAICALLY add f(x) to g(x) and call it h(x)
h(x) =____________________________
Now find h(1)=_______________
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2. 4.2 Notes.notebook February 19, 2013
Example)
Note: We would have to graph d(x) and p(x) to determine the range of each
with a calculator.
d) Find f(4), g(4), d(4), and p(4) to verify that the combined functions
do produce the correct values for the operations used.
Mar 16­11:01 AM
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3. 4.2 Notes.notebook February 19, 2013
Feb 15­3:19 PM
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4. 4.2 Notes.notebook February 19, 2013
Example)
Verify that the sum and product
function does produce the correct
value using x=4 and x=­3.
Again, we will need a calculator
to determine the range.
Mar 16­11:03 AM
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5. 4.2 Notes.notebook February 19, 2013
Look at the graph of q(x) on your calculator
and compare it to the equation for q(x).
Based on our work in the LAST 2 units we
understand why there is a vertical asymptote at
x=3.
This must be taken into consideration when we
state the domain for q(x).
Mar 16­11:21 AM
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6. 4.2 Notes.notebook February 19, 2013
Keep our previous discussion in mind for
this answer!
Mar 16­11:28 AM
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7. 4.2 Notes.notebook February 19, 2013
Let's see how creative you are:
You are now given the combined function and your job is to determine
the original functions!
Mar 16­11:31 AM
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8. 4.2 Notes.notebook February 19, 2013
These 2 are a little trickier!
Note: You cannot make your job easier by
making ONE of the functions =0.
Mar 16­11:32 AM
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9. 4.2 Notes.notebook February 19, 2013
Note: for Question b) your g(x) function CANNOT be as simple as g(x)=1
CAUTION: Since q(x) has NO restrictions on its domain or range,
the functions f(x) and g(x) you choose MUST produce a g(x) with NO
restrictions as well! Hmmm????
Mar 16­11:40 AM
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10. 4.2 Notes.notebook February 19, 2013
Again, be careful with
question b)
HINT: Make g(x) a function
which does NOT produce any
NON permissible values.
Mar 16­11:44 AM
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11. 4.2 Notes.notebook February 19, 2013
HOMEWORK: Page 278, #3,4,5a),6,7,8
9,10a)c),11 (use calc. for range)
12, 14.
Multiple Choice #1,2
Mar 16­11:44 AM
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