# Objectives Write functions using function notation.

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Objectives Write functions using function notation.
Evaluate and graph functions.

2. For the graph, evaluate ƒ(0), ƒ(.5) , and ƒ(–2).
1. For ƒ(x) = 5x + 3 Evaluate ƒ(0)= ƒ(-1)= 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) = x2 – 4x 4. Graph the function f(x) = 2x + 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?

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

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

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

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

Notes #3: Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2). ƒ(x) = x2 – 4x

Example 2A: 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.

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

Example 2C Graph the function. Graph the points. Do not connect the points because the values between the given points have not been defined.

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

Example 3A: 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) = 0.27x Replace the words with expressions.

Notes 3B: 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.

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) = 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.