Operations with Functions How do we add subtract

Operations with Functions • How do we add, subtract, multiply, and divide functions? • How do we write and evaluate composite functions? Holt. Mc. Dougal Algebra 2 Holt

Operations with Functions 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. Holt Mc. Dougal Algebra 2

Operations with Functions Holt Mc. Dougal Algebra 2

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

Operations with Functions Adding and Subtracting Functions 2 Given f(x) = 5 x – 6 and g(x) = x – 5 x + 6, find each function. 3. (f + g)(x) = f(x) + g(x) 2 = ( 5 x – 6) + ( x – 5 x + 6) = x 2 Substitute function rules. Combine like terms. 4. (f - g)(x) = f(x) - g(x) - 6) += ( 5 x – 6) ( x 2 + – 5 x + = - x + 10 x - 12 2 Holt Mc. Dougal Algebra 2 Substitute function rules. Change the signs Combine like terms.

Operations with Functions When you divide functions, be sure to note any domain restrictions that may arise. Holt Mc. Dougal Algebra 2

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

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

Operations with Functions Multiplying and Dividing Functions 2 Given f(x) = x + 2 and g(x) = x – 4, find each function. 7. (f g)(x) = f(x) ● g(x) 2 = (x + 2) (x – 4) Substitute function rules = x 3 + 2 x 2 – 4 x – 8 Use FOIL Pattern Holt Mc. Dougal Algebra 2

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

Operations with Functions Lesson 14. 1 Practice A Holt Mc. Dougal Algebra 2