1. Chapter 3
Graphs and Functions

2. Chapter Sections 3.1 – Graphs 3.2 – Functions
3.3 – Linear Functions: Graphs and Applications
3.4 – The Slope-Intercept Form of a Linear Equation
3.5 – The Point-Slope Form of a Linear Equation
3.6 – The Algebra of Functions
3.7 – Graphing Linear Inequalities
Chapter 1 Outline

3. The Algebra of Functions
§ 3.6
The Algebra of Functions

4. Operations of Functions
If f(x) represents one function, g(x) represents a second function ,and x is in the domain of both functions, then the following operations on functions may be performed:
Sum of functions: (f + g)(x) = f(x) + g(x)
Difference of functions: (f - g)(x) = f(x) - g(x)
Product of functions: (f•g)(x) = f(x)•g(x)
Quotient of functions:
Operations on Functions

5. Operations of Functions
Example:
If f(x) = x2 + x – 6 and g(x) = x - 3, then
(f + g)(x) = (x2 + x – 6) + (x – 3) = x2 + x – 6 + x – 3 = x2 + 2x - 9
(f - g)(x) = (x2 + x – 6) - (x – 3) = x2 + x – 6 – x + 3 = x2 - 3
(g - f)(x) = (x – 3) - (x2 + x – 6) = x – 3 – x 2 – x + 6 = -x2 + 3

6. Graph the Sums of Functions
Use the graph to find the value of the following:
a.) (f – g)(0) b.) (g + f )(-3) c.) (g • f )(-3)

7. Graph the Sums of Functions
a.) (f – g)(0)
= f (0) – g (0) = 2
+ 1
= 3

8. Graph the Sums of Functions
b.) (g + f )(-3) f g
= g(-3) + f (-3)
= 4 + (-1)
= 3
c.) (g • f )(2)
= g(2) • f (2)
= (-1) • (4)
= -4