Objectives Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.

Example 1: Using a Table to Write an Equation Determine a relationship between the x- and y-values. Write an equation. x y 5 10 15 20 1 2 3 4 Step 1 List possible relationships between the first x and y-values. Step 2 Write an equation. or

Check It Out! Example 1 Determine a relationship between the x- and y-values. Write an equation. {(1, 3), (2, 6), (3, 9), (4, 12)} x 1 2 3 4 y 3 6 9 12 Step 1 List possible relationships between the first x- and y-values. Step 2 Write an equation. y = 3x

The input (x values) of a function is the independent variable. The output (y values) of a function is the dependent variable. The dependent variable depends on the independent variable. Ex: Your grade in math depends on your test scores (NOT your test score depend on your math grade) The y values change BECAUSE the x values change. (Your grade changes because of your test scores)

Example 2A: Identifying Independent and Dependent Variables Identify the independent and dependent variables in the situation. A painter must measure a room before deciding how much paint to buy. Think about what changes based on the other thing The amount of paint depends on the measurement of a room. Dependent: amount of paint Independent: measurement of the room

Check It Out! Example 2a Identify the independent and dependent variable in the situation. A company charges $10 per hour to rent a leaf blower. Think about what you are able to change in this problem – the cost or the hours (because you are an independent person) The cost to rent a leaf blower depends on the length of time it is rented. Dependent variable: cost Independent variable: time

Example 3A: Writing Functions Identify the independent and dependent variables. Write a rule in function notation for the situation. Instead of y, we write f(x) A math tutor charges $35 per hour. “f of x” The amount a math tutor charges depends on number of hours. Dependent: charges Independent: hours Let h represent the number of hours of tutoring. The function for the amount a math tutor charges is f(h) = 35h.

Example 3B: Writing Functions Identify the independent and dependent variables. Write a rule in function notation for the situation. A fitness center charges a $100 initiation fee plus $40 per month. The total cost depends on the number of months, plus $100. Dependent: total cost Independent: number of months Let m represent the number of months The function for the amount the fitness center charges is f(m) = 40m + 100.

Example 4A: Evaluating Functions Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. f(x) = 3(x) + 2 f(x) = 3(x) + 2 Substitute 7 for x. Substitute –4 for x. f(7) = 3(7) + 2 f(–4) = 3(–4) + 2 = 21 + 2 Simplify. Simplify. = –12 + 2 = 23 = –10

Check It Out! Example 4a Evaluate the function for the given input values. For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. h(c) = 2c – 1 h(c) = 2c – 1 h(1) = 2(1) – 1 h(–3) = 2(–3) – 1 = 2 – 1 = –6 – 1 = 1 = –7

Example 5: Finding the Reasonable Range and Domain of a Function Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each. Write a function to describe the situation. Find a reasonable domain and range of the function. Money spent is $15.00 for each DVD. f(x) = $15.00 • x If Joe buys x DVDs, he will spend f(x) = 15x dollars. Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {1, 2, 3}.

Check It Out! Example 5 The settings on a space heater are the whole numbers from 0 to 3. The total of watts used for each setting is 500 times the setting number. Write a function rule to describe the number of watts used for each setting. Number of watts used is 500 times the setting #. watts f(x) = 500 • x For each setting, the number of watts is f(x) = 500x watts.

Assignment: Pg 249 (3-25 odd)