1 7 Function Notation Objectives Write functions using

1 -7 Function Notation Objectives Write functions using function notation. Evaluate and graph functions. Holt Algebra 2

1 -7 Function Notation 1. For ƒ(x) = 5 x + 3 ƒ(-1)= Evaluate ƒ(0)= and ƒ(– 2) = 2. For the graph, evaluate ƒ(0), ƒ(. 5) , and ƒ(– 2). 3. Evaluate ƒ(0), ƒ , and ƒ(– 2) for ƒ(x) = x 2 – 4 x 4. Graph the function f(x) = 2 x + 1. 5. A painter charges $200 plus $25 for each can of paint used. a. Write a function to represent the total charge for a certain number of cans of paint. b. Evaluate f(4), and state what it represents? Holt Algebra 2

1 -7 Function Notation The function described by ƒ(x) = 5 x + 3 is the same as the function described by y = 5 x + 3. And both of these functions are the same as the set of ordered pairs (x, 5 x+ 3). y = 5 x + 3 (x, y) ƒ(x) = 5 x + 3 (x, ƒ(x)) Holt Algebra 2 (x, 5 x + 3) Notice that y = ƒ(x) (x, 5 x + 3) for each x.

1 -7 Function Notation Example 1: Evaluating Functions For each function, evaluate ƒ(0), ƒ – 2). ƒ(x) = 8 + 4 x Substitute each value for x and evaluate. ƒ(0) = 8 + 4(0) = 8 ƒ =8+4 = 10 ƒ(– 2) = 8 + 4(– 2) = 0 Holt Algebra 2 , and ƒ(

1 -7 Function Notation Notes #1: Notation and Evaluating Functions ƒ(x) = 5 x + 3 ƒ of x equals 5 times x plus 3. f(1)= 8 for f(x) = 5 x + 3 (1, 8) for y = 5 x + 3 For the function, evaluate ƒ(0)= ƒ(-1)= and ƒ(– 2) = Holt Algebra 2

1 -7 Function Notation Notes #2: Evaluating Functions For each function, evaluate ƒ(0), ƒ – 2). Use the graph to find the corresponding y-value for each x-value. ƒ(0) = 3 ƒ =0 ƒ(– 2) = 4 Holt Algebra 2 , and ƒ(

1 -7 Function Notation Notes #3: Evaluating Functions For each function, evaluate ƒ(0), ƒ – 2). ƒ(x) = x 2 – 4 x Holt Algebra 2 , and ƒ(

1 -7 Function Notation Example 2 A: Graphing Functions Graph the function. {(0, 4), (1, 5), (2, 6), (3, 7), (4, 8)} Graph the points. Do not connect the points because the values between the given points have not been defined. Holt Algebra 2

1 -7 Function Notation Example 2 B: Graphing Functions Graph the function f(x) = 3 x – 1. Make a table. Graph the points. x 3 x – 1 f(x) – 1 3(– 1) – 1 – 4 0 3(0) – 1 1 3(1) – 1 2 Connect the points with a line because the function is defined for all real numbers. Holt Algebra 2

1 -7 Function Notation Example 2 C Graph the function. 3 5 7 9 2 6 10 Graph the points. Do not connect the points because the values between the given points have not been defined. Holt Algebra 2

1 -7 Function Notation Notes #4: Graphing Functions Graph the function f(x) = 2 x + 1. Graph the points. Make a table. x 2 x + 1 f(x) – 1 2(– 1) + 1 – 1 0 2(0) + 1 1 1 2(1) + 1 3 Connect the points with a line because the function is defined for all real numbers. Holt Algebra 2

1 -7 Function Notation Example 3 A: Function Application A local photo shop will develop and print the photos from a disposable camera for $0. 27 per print. Write a function to represent the cost of photo processing. Let x be the number of photos and let f be the total cost of the photo processing in dollars. Identify the variables. Cost depends on the number of photos processed Cost = 0. 27 number of photos processed f(x) = 0. 27 x Holt Algebra 2 Replace the words with expressions.

1 -7 Function Notation Notes 3 B: Function Application A local photo shop will develop and print the photos from a disposable camera for $0. 27 per print. What is the value of the function for an input of 24, and what does it represent? f(24) = 0. 27(24) Substitute 24 of x and simplify. = 6. 48 The value of the function for an input of 24 is 6. 48. This means that it costs $6. 48 to develop 24 photos. Holt Algebra 2

1 -7 Function Notation Notes #5: Function Application A painter charges $200 plus $25 for each can of paint used. a. Write a function to represent the total charge for a certain number of cans of paint. t(c) = 200 + 25 c b. What is the value of the function for an input of 4, and what does it represent? 300; total charge in dollars if 4 cans of paint are used. Holt Algebra 2