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**Objectives Write functions using function notation.**

Evaluate and graph functions.

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**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?

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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)

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**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

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**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) =

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**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

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**Notes #3: Evaluating Functions**

For each function, evaluate ƒ(0), ƒ , and ƒ(–2). ƒ(x) = x2 – 4x

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**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.

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**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.

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

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**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.

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**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.

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**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.

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**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.

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Functions and Their Representations

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