Chapter 3 Graphs and Functions

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

The Algebra of Functions § 3.6 The Algebra of Functions

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

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

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)

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

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