The arithmetic combination of functions is similar to the combination of real numbers. It is commonly seen in the real world to calculate the number of supplies a company has, or various other types of payment methods.
There are 4 types of Arithmetic Combinations, and they are as follows:
Sum
Difference
Product
Quotient
How do we use these functions in a problem you may ask?
Sum:
Ex. Find
for the functions:
for the functions:
and 
Make sure to combine all like terms and distribute negative signs appropriately!!
If you were to graph this equation it would look like this:
Difference:
Ex. Find
for the functions:
for the functions:
and 
Make sure to combine all like terms and distribute negative signs appropriately!!
If you were to graph this equation it would look like this:
Product:
Ex. Find 
for the functions:
for the functions:
and
Tip: When distributing, use the FOIL method (first, outside, inside, last)
If you were to graph this equation it would look like this:
Quotient
Ex. Find 
for the functions:
for the functions:
and 
The second part of the answer for quotient arithmetic combination problems is the domain.
To find the domain:
1. Set the denominator of the quotient equal to zero
2. Solve for 'x'
Ex.
**This will often be a follow-up question when you are finding the quotient**
If you were to graph this equation it would look like this:
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