Introduction to Functions Mathematical Functions 1

Remember Me … remember Me Psst … my previous name was ‘y’

Example

Key Terms Function – A pairing of two sets of numbers. The first set of numbers is paired with exactly one element of the second set. Say huh????? ….. otra vez 4

This is a function: Each input has one output

Function take three….. 2 3 5 4 1 10 2 3 5 4 1 10 2 6 7 2 6 7 input output 2 3 5 4 1 10 input output 2 6 7 2 6 7

Some inputs have more than one output This is not a function: Some inputs have more than one output 5 7 9 2 3 input output 2 3 5 7 9

Examples Determine if a set of ordered pairs represents a function: {(3,4), (3,6), (5, 14), (7, 4)} Not a function – An input of 3 gives 2 different outputs. {(4,12), (3, 7), (5, 2), (3, 7), (8, 12)} Is a function – Each input has one and only one output. 8

Function Machine input output

Function input output

Function input output

NOT input output

NOT a function Stop …. Lets practice Function 1. 2. 2 3 9 4 5 7 9 2.2 input output 2. 2.2 26 3 2 9 NOT a function

Key Terms Domain – The first coordinate in a set of ordered pairs. Known as the 'x' value, the input, left to right on the graph. Range – The second coordinate in a set of ordered pairs. Known as the 'y' value, the output, top to bottom on the graph 14

Function Machine input output x Domain independent y Range dependent

Domain All real values for x x

Range All real values for y y

Example 1 Identify the domain and range of the function. Input (pounds) 1.5 2.3 3.1 4.2 Output (dollars) $7.80 $11.96 $16.12 $21.82

Now try guided practice 1-3, p. 7. Answer Domain: 1.5, 2.3, 3.1, 4.2 Range: 7.80, 11.96, 16.12, 21.82 Now try guided practice 1-3, p. 7.

Example 2 The domain of the function y = x-3 is 2, 5, 8, and 11. make a table for the function, then identify the range of the function.

Work on Guided Practice 4 and 5, p. 8. Answer X 2 5 8 11 Y = x-3 2-3 = -1 5-3 = 2 8-3 = 5 11-3 = 8 Work on Guided Practice 4 and 5, p. 8.

Example 3 Write a rule for the function Input 3 6 7 10 Output 15 30 35 50 Hint: Look at what is being done to the input values in order to achieve the outputs values.

Try Guided Practice 6 and 7, p. 8. Answer The input values are multiplied by 2 in order to get the output values. Let Input = x Output = y Therefore: y = 5x Try Guided Practice 6 and 7, p. 8.

Examples T = time C = cost c = 5t + 10 The table below shows the amount that a company charges for raft rental for up to 10 hours. Find an equation to represent the function. List the domain and range values. T = time C = cost c = 5t + 10 Domain = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Range = {15, 20, 25, 30, 35, 40, 45, 50, 55, 60} 24

Assignment