# 1-1 Operations on real numbers TOPIC 3 LINEAR FUNCTIONS IN THIS CHAPTER I CAN 3-1: identify the domain and range and understand a relation has a oneto-one relationship 3-2: write and graph linear functions and determine the domain and range 3-4: write arithmetic sequences in recursive and explicit forms

3-5: use technology to find a best fit line and interpret the function 3-6: use technology to compute and interpret the correlation coefficient for linear data 3-1 RELATIONS AND FUNCTIONS HOMEWORK: 5-7, 13-17

WARM-UP Whats a reasonable number of rows? 3-7 Whats a reasonable number of desks?15-35 Desks WARM-UP Rows VOCABULARY

Relation a set of ordered (3,15), (4,20), (5,25), (6,30), (7,3 pairs x (input) Function a relation where y each input has only one output (output) Domain the set of inputs (xvalues) Range the set of outputs (yvalues) 3 4

5 6 7 15 20 25

30 35 D: {3, 4, 5, 6, 7} R: {15, 20, 25, 30, 35} EXAMPLE Mr. Trimble is filling up his backyard pool with water. The hose pumps 10 gallons of water every minute. The pool holds 10,000 gallons. What is a reasonable domain (time) and range (water)? Domain would be every minute between 0 and 1,000 minutes.

Range would be every gallon of water between 0 and 10,000. Gallons of Water EXAMPLE Time (minutes) VOCABULARY Continuous Function when the domain includes all real numbers. The graph is a line or curve. Discrete Function when the domain consists of just whole integers. The graph is a series of data

points. 3-1 RELATIONS AND FUNCTIONS HOMEWORK: 18-24 WARM-UP (1, 2), (5, 6), (7, 1), (8,1 0) 2 (1, 2), (5, 6), (7, -1), (8, 0), (8, -1) 1

2 5 6 5 6 7 -1

7 -1 8 0 8 0

WHAT IS A FUNCTION? VOCABULARY One to One no two elements in the domain have the same element in the range. (-2,5) 5 (3,6) 2

(4,7) 3 7 (5,7) 4 5 6

Functio YES n? NO One to One? TO RECAP A function is when each domain element has one range element (one arrow touches each number in the domain) It is one to one when each range element has one domain element (one arrow touches each number in the range)