4.3 Writing Functions Objectives Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values. Vocabulary independent variable dependent variable function rule function notation

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 How do we go from 5 to 1? method works for all x and y? Equation Does equation represent a function?

Example 2A: Identifying Independent and Dependent Variables The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable. 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. What are our two variables? Then complete the sentence: The depends on the Dependent: Independent: The height of a candle decrease d centimeters for every hour it burns.

Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable x-values y-values Domain Range Input Output x f(x) The dependent variable is a function of the independent variable. y is a function of x. y = f(x) y = f (x) An algebraic expression that defines a function is a function rule.

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

Example 4A: Evaluating Functions input You can think of a function as an input-output machine. x 2 What is the machine doing to the inputs? 6 Example 4A: Evaluating Functions function f(x)=5x Evaluate the function for the given input values. For f(x) = 3x + 2, find f(7) and f(-4). f(x) = 3(x) + 2 5x Substitute 7 for x. f(7) = 3(7) + 2 10 f(–4) = 30 output = 21 + 2 Simplify. = 23

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. How many DVDs will Joe buy? So what are our variable? 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}. Could 1.5 be one of the x-values in the domain? What is the range? x 1 2 3 f(x) 15(1) = 15 15(2) = 30 15(3) = 45