Warm-up 1.7 Evaluate the equation y = 2x + 7 for: X = -2 X = 5 X = ½ 1.7 Function Notation

HW Review 1.7 Function Notation

1.7 Function Notation Objective: TSWBAT write functions using function notation Determine an appropriate linear model for a real-life situation

Function Notation Some sets of ordered pairs can be described by using an equation. We can represent these using function notation.

Function Notation ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 Output value Input value Output value Input value ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 ƒ of x equals 5 times x plus 3. ƒ of 1 equals 5 times 1 plus 3.

Function Notation The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3. y = 5x + 3 is the same as ƒ(x) = 5x + 3

Function Notation The graph of a function is a picture of the function’s ordered pairs on a coordinate plane.

Caution f(x) is not “f times x” or “f multiplied by x.” f(x) means “the value of f at x.” So f(1) represents the value of f at x =1 Caution

Example 1 For each function, evaluate ƒ(0), ƒ , and ƒ(–2). ƒ(x) = 8 + 4x Substitute each value for x and evaluate. ƒ(0) = 8 + 4(0) = 8 ƒ = 8 + 4 = 10 ƒ(–2) = 8 + 4(–2) = 0

Dependent and Independent Variables The output f(x), is the dependent variable because it depends on the input value of the function. The input x, is called the independent variable.

Graphing a Function Independent variable x, is graphed on the horizontal axis Dependent variable f(x), is graphed on the vertical axis.

Linear Models Most cell phone rate plans are a linear function of some kind. Example plan: you pay $20 a month for your cell phone and 5 cents per minute of usage The monthly cost of using your cell phone would be a linear equation or a function, C, based on the number of minutes you use monthly and the monthly phone cost.

Linear Models Can you come up with a linear model (function) in slope-intercept form that correctly models the rate plan described? What variables do you choose? Why? Which variable is the dependent variable? Why? Independent variable? Why?

Check 1. f(x) = 9 – 6x 9; 6; 21 2. 4; 6; 0 3. Graph f(x)= 4x + 2. For each function, evaluate 1. f(x) = 9 – 6x 9; 6; 21 2. 4; 6; 0 3. Graph f(x)= 4x + 2. 1.7 Function Notation

Making a Linear Model from a real-life situation Identify the Independent (x) and dependent (y) variable Make a function Make a table of values! Graph to show visually! 1.7 Function Notation

Example 1 You make $25 an hour babysitting Write a function that represents this situation Graph it! 1.7 Function Notation

Example 2 You receive $50 from your grandmother. Afterwards, She will give you $5 a week for allowance Write a function representing this scenario What is the independent variable represent? The dependent? 1.7 Function Notation

Example 3 In 2013, Kapernick was paid around $50,000 per game. Write a function showing this scenario. 1.7 Function Notation

Example 4 You are selling tickets to the school dance. Each ticket costs $10. You have $20 left over from last year’s ticket sales. Write a function that represents this scenario. 1.7 Function Notation

Example 5 Today you are 40 inches tall, if you grow at a rate of 2 inches per year, write a function demonstrating this scenario. Graph it! 1.7 Function Notation

Example 6 You are really hungry. You just had a really long workout. You go to In and Out and you really want burgers, animal style. There are 330 calories per burger. Make a linear model representing this scenario. Graph it. 1.7 Function Notation

Example 7 You weigh 175 pounds. With each animal burger you eat, you will gain 1 more pound. Write a function representing this situation. 1.7 Function Notation

Example 8 Ms. Stine is having a quiz on Friday. You get 5 points for every correct question. Write a linear model representing this situation If there are 21 questions, what is the maximum score you can get 1.7 Function Notation

Example 9 It is midday and it is 90 degrees outside. Every hour, the temperature drops 5 degrees. Write a linear model representing this situation. What domain makes sense? Range? 1.7 Function Notation

Example 10 Devin is unhappy that he does not have a girlfriend. He decides to go on 2 OKCupid dates a week. Make a linear model for this situation. What is a reasonable domain? Range? 1.7 Function Notation

Reflection Let’s say we are going on a trip. We are driving and we average 60 miles per hour. What function would correctly model the distance (D) we travel in a certain number of hours (t)?

Homework Page 55 Page 56 Page 95 21, 22, 33, 34, 36 45-48 48 a, b, and c 1.7 Function Notation

Homework 1.7 Function Notation