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4.6 Formalizing relations and functions

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 1. Relation: pairing of numbers in one set (the domain) with numbers in another set (the range). (often put in an ordered pair). Domain:.

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4.6 Formalizing relations and functions

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  1. 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 1

  2. Relation: pairing of numbers in one set (the domain) with numbers in another set (the range). (often put in an ordered pair) Domain: The input values (x-values) Range: The output values (y-values) Example: a motion detector stores input values (times) and output values (heights) as an egg is tracked as it is dropped from 10 ft. above the ground. {(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)} {(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)} Domain: {0, .1, .2, .3} {8.6, 9.4, 9.8, 10} Range:

  3. Find the domain and range and determine if the relation is a function. Function: a relation where one value in the domain is paired with exactly one value of the range. Domain: {2, 6, 9, 10} Range: {4, 8, 11, 13} Yes, it’s a function Domain: {2, 6, 10, 11} Range: {9} Yes, it’s a function Domain: {2, 7, 9} Range: {3, 4, 5, 6} NO, it’s not a function

  4. Are the following graphs functions? –use the vertical line test function Not a function

  5. Are the following graphs functions? Use the vertical line test function Not a function Pg 271: 1,2,7-15, 48-50

  6. {(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)} Use a mapping diagram to determine whether the relation is a function. Domain: {0, .1, .2, .3} {10, 9.8, 9.4, 8.6} Range: Pg 271: 1,2,7-15, 48-50 Domain: Range: 10 9.8 9.4 8.6 0 .1 .2 .3 function:? YES

  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)

  8. 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

  9. Evaluating a Function Find each function value for f(x) = 4x + 8 a. f(3) f(3) = 4(3) + 8 f(3) = 12 + 8 f(3) = 20 • f(-5) f(-5) = 4(-5) + 8 f(-5) = -20 + 8 f(-5) = -12 Given g(x) = -7x + 5; find g(2) g(2) = -7(2) + 5 g(2) = -14 + 5 g(2) = -9

  10. 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(x) = 250x w() = 250( ) Assignment: pg 271 ( 1-3, 8-17, 26,27,31-34) 8 8 w( 8 ) = 2000 What does w(8) = 2000 mean? You can read 2000 words in 8 minutes.

  11. assignment • pg 271 ( 1-3, 8-17,26,27,31-34)

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