TOPIC 3 LINEAR FUNCTIONS IN THIS CHAPTER I

  • Slides: 14
Download presentation
TOPIC 3 – LINEAR FUNCTIONS

TOPIC 3 – LINEAR FUNCTIONS

IN THIS CHAPTER I CAN… • 3 -1: identify the domain and range and

IN THIS CHAPTER I CAN… • 3 -1: identify the domain and range and understand a relation has a one-to-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

3 -1 RELATIONS AND FUNCTIONS HOMEWORK: 5 -7, 13 -17

WARM-UP What’s a reasonable number of rows? 3 -7 What’s a reasonable number of

WARM-UP What’s a reasonable number of rows? 3 -7 What’s a reasonable number of desks? 15 -35

Desks WARM-UP Rows

Desks WARM-UP Rows

VOCABULARY • Relation – a set of ordered pairs (3, 15), (4, 20), (5,

VOCABULARY • Relation – a set of ordered pairs (3, 15), (4, 20), (5, 25), (6, 30), (7, 35 • Function – a relation where each input has only one output • Domain – the set of inputs (xvalues) • Range – the set of outputs (yvalues) x (input) 3 4 5 6 7 y (output) 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

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)

Gallons of Water EXAMPLE Time (minutes)

VOCABULARY • Continuous Function – when the domain includes all real numbers. The graph

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

3 -1 RELATIONS AND FUNCTIONS HOMEWORK: 18 -24

WARM-UP (1, 2), (5, 6), (7, -1), (8, 0) 1 2 (1, 2), (5,

WARM-UP (1, 2), (5, 6), (7, -1), (8, 0) 1 2 (1, 2), (5, 6), (7, -1), (8, 0), (8, -1) 1 2 5 6 7 -1 8 0

WHAT IS A FUNCTION?

WHAT IS A FUNCTION?

VOCABULARY • One to One – no two elements in the domain have the

VOCABULARY • One to One – no two elements in the domain have the same element in the range. (-2, 5) -2 5 (3, 6) 3 6 (4, 7) 4 7 (5, 7) 5 Function YES ? NO One to One?

TO RECAP • A function is when each domain element has one range element

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)