1. Operations with Functions
Essential Questions
How do we add, subtract, multiply, and divide functions?
How do we write and evaluate composite functions?
Holt McDougal Algebra 2
Holt Algebra2

2. You can perform operations on functions in much the same way that you perform operations on numbers or expressions. You can add, subtract, multiply, or divide functions by operating on their rules.

4. Adding and Subtracting Functions
Given f(x) = 4x2 + 3x – 1 and g(x) = 6x + 2, find each function.
1. (f + g)(x)
(f + g)(x) = f(x) + g(x)
= (4x2 + 3x – 1) + (6x + 2)
Substitute function rules.
= 4x2
+ 9x
+ 1
Combine like terms.
2. (f - g)(x)
(f - g)(x) = f(x) - g(x)
Substitute function rules. - -
= (4x2 + 3x – 1) - ( 6x + 2) +
Change the signs
- 3x
- 3
= 4x2
Combine like terms.

5. Adding and Subtracting Functions
Given f(x) = 5x – 6 and g(x) = x2– 5x + 6, find each function.
3. (f + g)(x)
(f + g)(x) = f(x) + g(x)
= ( 5x – 6) + ( x2 – 5x + 6)
Substitute function rules.
= x2
Combine like terms.
4. (f - g)(x)
(f - g)(x) = f(x) - g(x)
Substitute function rules. - -
= ( 5x – 6) - ( x2 – 5x + 6) + +
Change the signs
= - x2
- 12
+ 10x
Combine like terms.

6. When you divide functions, be sure to note any domain restrictions that may arise.

7. Multiplying and Dividing Functions
Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find each function.
5. (f g)(x)
(f g)(x) = f(x) ● g(x)
= (6x2 – x – 12) (2x – 3)
Substitute function rules
= 12x3
– 18x2
– 2x2
+ 3x
– 24x
+ 36
Distributive Property
= 12x3
– 20x2
– 21x
+ 36
Combine like terms.

8. Multiplying and Dividing Functions
Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find each function.
Set up the division as a rational expression.
( )
(x) f g 6.
Factor; then divide out common factors.
Note domain restrictions

9. Multiplying and Dividing Functions
Given f(x) = x + 2 and g(x) = x2 – 4, find each function.
7. (f g)(x)
(f g)(x) = f(x) ● g(x)
= (x + 2) (x2 – 4)
Substitute function rules
Use FOIL Pattern
= x3
+ 2x2
– 4x
– 8

10. Multiplying and Dividing Functions
Given f(x) = x + 2 and g(x) = x2 – 4, find each function.
Set up the division as a rational expression.
( )
(x) f g 8.
Factor; then divide out common factors.
Note domain restrictions

11. Lesson 14.1 Practice A