3-3 Writing Functions Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

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 or y-values. 5 – 4 = 1 or

Example 1 Continued Step 2 Determine if one relationship works for the remaining values. 10 – 4  2 and 15 – 4  3 and 20 – 4  4 and The value of y is one-fifth, , of x. Step 3 Write an equation. or The value of y is one-fifth of x.

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- or y-values. 1  3 = 3 or 1 + 2 = 3

Check It Out! Example 1 Continued Step 2 Determine if one relationship works for the remaining values. 2 • 3 = 6 3 • 3 = 9 4 • 3 = 12 2 + 2  6 3 + 2  9 4 + 2  12 The value of y is 3 times x. Step 3 Write an equation. y = 3x The value of y is 3 times x.

The equation in Example 1 describes a function because for each x-value (input), there is only one y-value (output).

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. The amount of paint depends on the measurement of a room. Dependent: amount of paint Independent: measurement of the room

Example 2B: Identifying Independent and Dependent Variables Identify the independent and dependent variables in the situation. The height of a candle decreases d centimeters for every hour it burns. The height of a candle depends on the number of hours it burns. Dependent: height of candle Independent: time

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)

Check It Out! Example 2a Identify the independent and dependent variable in the situation. A company charges $10 per hour to rent a jackhammer. The cost to rent a jackhammer depends on the length of time it is rented. Dependent variable: cost Independent variable: time

Check It Out! Example 2b Identify the independent and dependent variable in the situation. Apples cost $0.99 per pound. The cost of apples depends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

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

Example 4B: Evaluating Functions Evaluate the function for the given input values. For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2. g(t) = 1.5t – 5 g(t) = 1.5t – 5 g(6) = 1.5(6) – 5 g(–2) = 1.5(–2) – 5 = 9 – 5 = –3 – 5 = 4 = –8

Example 4C: Evaluating Functions Evaluate the function for the given input values. For , find h(r) when r = 600 and when r = –12. = 202 = –2

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

Check It Out! Example 4b Evaluate the function for the given input values. For g(t) = , find g(t) when t = –24 and when t = 400. = –5 = 101

Lesson Quiz: Part III Write a function to describe the situation. Find the reasonable domain and range for the function. 5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour. f(h) = 200h + 100 Domain: {2, 3, 4} Range: {$500, $700, $900}