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Warm- UP

Warm- UP. F(x) = x + 2, g(x) = -x + 3 Add the two functions Subtract the two functions Multiply the two functions.

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Warm- UP

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  1. Warm- UP F(x) = x + 2, g(x) = -x + 3 • Add the two functions • Subtract the two functions • Multiply the two functions

  2. Math IV Lesson 4 Essential Question: How do you combine two functions to form another functionSection objectives: Students will learn how to find the sum, difference, product, quotient, and composition of two functions. Standards:MM4A4. Students will investigate functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

  3. 1.5 Combinations of Functions Sum of functions (f + g) (x) = f(x) + g(x) Difference of functions (f – g) (x) = f(x) – g(x) Product of functions Fg(x) = f(x) g(x)

  4. Finding the sum of 2 functions If f(x) = 2x + 1, and g(x) = x2 + 2x – 1 Find (f+g) (x) when x = 2 (f + g) (x) = f(x) + g(x) = 2x + 1 + x2 + 2x – 1 = x2 + 4x Now plug in 2 (2)2 + 4(2) = 4 + 8 = 12

  5. Finding the difference of two functions If f(x) = 2x + 1 , and g(x) = x2 + 2x – 1 Find (f – g)(x) when x = 2 (f – g) (x) = f(x) – g(x) = 2x + 1 – (x2 + 2x – 1) = 2x + 1 - x2 - 2x + 1 = - x2 + 2 Now plug in 2 -(2)2 + 2 = -4 + 2 = -2

  6. Finding the Product of two functions Given f(x) = x2 and g(x) = x – 3 Find fg(x) when x = 4 fg(x) = f(x) g(x) = (x2) (x-3) = x3 – 3x2 Now plug in 4 (4)3 – 3(4)2 = 16

  7. Finding the quotient of two functions Given f(x) = √(x) and g(x) = √(4-x2). Find f/g(x) f/g (x) = f(x) / g(x) = √(x) / √(4-x2)

  8. Compositions of functions The composition of the function f with the function g is (f ◦ g) (x) = f(g(x)) Here you plug one function into another function. Always plug the right function into the left.

  9. Examples • Given f(x) = x + 2, and g(x) = 4-x2 • Find (f◦g)(x) when x = 2 2. Find (g◦f) (x) when x = 1

  10. Another Example • Given f(x) = x2 – 9 and g(x) = √(9-x2) • Find (f◦g)(x)

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