3 3 Writing Functions Holt 1 Algebra 1

3 -3 Writing Functions Holt 1 Algebra 1 Holt. Algebra Mc. Dougal

3 -3 Writing Functions Bell Ringer and Engage Determine if each graph is a function Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Quick tip: Easy way to determine if a graph is a function – remember the definition of a FUNCTION A function is a special type of relation that pairs each domain value with exactly one range value. So each x-value has exactly one y-value Holt Mc. Dougal Algebra 1

3 -3 Writing Functions VERTICAL LINE TEST If you can draw a vertical line anywhere on the graph, and it hits the graph in more than one place, the graph is NOT a function Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Explore Suppose you are baby sitting and charges $5 per hour. Below is a table of values describing how much money you make. Time worked x Amount Earned y 1 5 2 10 3 15 4 20 1) Plot a discrete function on a coordinate plane 2) Attempt to write an equation using two different variables to show this relationship. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Explain Using a Table to Write an Equation Determine a relationship between the x- and y -values. Write an equation. x 5 y 1 10 15 20 2 3 4 Step 1 List possible relationships between the first x or y-values. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Explain 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. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Explain Continued 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 Holt Mc. Dougal Algebra 1

3 -3 Writing Functions 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 = 3 x The value of y is 3 times x. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Vocab independent variable: The input of a function dependent variable: The output of a function The value of the dependent variable depends on, or is a function of, the value of the independent variable. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Helpful Hint There are several different ways to describe the variables of a function. Independent Variable x-values Dependent Variable y-values Domain Range Input Output x f(x) ASK: which one depends on the other? ? Holt Mc. Dougal Algebra 1

3 -3 Writing Functions 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 Holt Mc. Dougal Algebra 1

3 -3 Writing Functions 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 Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Elaborate Function Notation The dependent variable is a function of the independent variable. y is y = a function of f y = f(x) Holt Mc. Dougal Algebra 1 x. (x)

3 -3 Writing Functions Elaborate Identify the independent and dependent variables. Write an equation 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) = 40 m + 100. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Elaborate You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5 x. If you input a value x, the output is 5 x. Holt Mc. Dougal Algebra 1 input x 2 6 function f(x)=5 x 10 5 x 30 output

3 -3 Writing Functions Elaborate Evaluate the function for the given input values. For f(x) = 3 x + 2, find f(x) when x = 7 and when x = – 4. f(x) = 3(x) + 2 f(7) = 3(7) + 2 Substitute 7 for x. = 21 + 2 Simplify. = 23 Holt Mc. Dougal Algebra 1 f(x) = 3(x) + 2 f(– 4) = 3(– 4) + 2 Substitute – 4 for x. Simplify. = – 12 + 2 = – 10

3 -3 Writing Functions When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people. Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Lesson Quiz: Part I Identify the independent and dependent variables. Write an equation in function notation for each situation. 1. A buffet charges $8. 95 person. independent: number of people dependent: cost f(p) = 8. 95 p 2. A moving company charges $130 for weekly truck rental plus $1. 50 per mile. independent: miles dependent: cost f(m) = 130 + 1. 50 m Holt Mc. Dougal Algebra 1

3 -3 Writing Functions Lesson Quiz: Part II Evaluate each function for the given input values. 3. For g(t) = , find g(t) when t = 20 and when t = – 12. g(20) = 2 g(– 12) = – 6 4. For f(x) = 6 x – 1, find f(x) when x = 3. 5 and when x = – 5. f(3. 5) = 20 f(– 5) = – 31 Holt Mc. Dougal Algebra 1