4.6 Formalizing relations and functions To determine whether a relation is a function AND to find the domain and range using function notation. Day 2

Function notation: uses parenthesis to name the input or independent variable for the function. f(x) is pronounced f of x It does not mean to multiply f and x together. y = f(x) Equation y = 4x + 8 y = -7x + 5 y = 5x – 7 Function Notation f(x) = 4x + 8 g(x) = -7x + 5 h(x) = 5x – 7

Function Notation Name a fast car New School: Function Notation f(x) = 2x + 3 f(4) = 2(4) + 3 f(4) = 8 + 3 f(4) = 11 (4, 11) Name a slow car Old School: Equation y = 2x + 3 Solve y = 2x + 3 when x = 4 y = 2(4) + 3 y = 8 + 3 y = 11 (4, 11)

Evaluating a Function Find each function value for f(x) = 4x + 8 Given g(x) = -7x + 5; find g(2) g(2) = -7(2) + 5 g(2) = -14 + 5 g(2) = -9

Find the range of the function for the given domain. The domain of f(x) = 4x - 12 is {1,3,5,7,9}. What is the range? (use a table) x 4x - 12 f(x) 1 4( ) - 12 1 -8 3 4( ) - 12 3 5 4(5 ) - 12 8 7 4( 7) - 12 16 9 4( 9) - 12 24 What is the range? {-8, 0, 8, 16, 24}

f(x) = -1.5x + 4 f(1) = -1.5(1)+ 4 f(1) = = 2.5 Pg 271: 3-5, 18-21 The domain of f(x) = -1.5x + 4 is {1,2,3,4}. What is the range? Use function notation f(x) = -1.5x + 4 f(1) = -1.5(1)+ 4 f(1) = = 2.5 Pg 271: 3-5, 18-21 f(2) = f(2) = -1.5(2)+ 4 = 1 f(3) = f(3) = -1.5(3)+ 4 = -.5 f(4) = -1.5(4)+ 4 f(4) = = -2 The range is: {-2, -.5, 1, 2.5}

You can read 2000 words in 8 minutes. Evaluating a function The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8 min? w(x) = 250x w( ) = 250( ) w(x) = 250x 8 8 w( 8 ) = 2000 What does w(8) = 2000 mean? You can read 2000 words in 8 minutes.

0 < q < 3 q 3 0 < A(q) < 300 A(q) A(0) = 100(0) You have 3 qt of paint to paint the trim in your home. A quart of paint covers 100ft2. The function A(q) = 100q represent the area A(q), in square feet, that q quarts of paint cover. What domain and range are reasonable for the function? What is the graph of the function? KNOW NEED PLAN Have 3 qt of paint Reasonable domain and range values Find least and greatest amounts of paint. Make a graph. 1 qt covers 100ft2 Domain: variable? Smallest amount? Largest amount? 0 < q < 3 q 3 Range: variable? Smallest amount? Largest amount? 0 < A(q) < 300 A(q) A(0) = 100(0) A(3) = 100(3) A(0) = 0 A(3) = 300 Paint usage q A(q) 1 2 3 300 200 100 Area 100 page 271: 4,5, 18-24, 28,29 200 1 2 3 300 Paint used (qt) q

Assignment: pg 271 ( 3, 16-21,26,27,31-34,41)