Objectives Vocabulary 1.7 Function Notation

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Objectives Vocabulary 1.7 Function Notation Write functions using function notation. Evaluate and graph functions. Vocabulary function notation dependent variable independent variable

ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 ƒ of x equals 5 times x plus 3. When x = 4 evaluate y = 5x + 3 Output value Input value Output value Input value ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 ƒ of x equals 5 times x plus 3. ƒ of 1 equals 5 times 1 plus 3. y = 5x + 3 (x, y) (x, 5x + 3) Notice that y = ƒ(x) for each x. ƒ(x) = 5x + 3 (x, ƒ(x)) (x, 5x + 3) The graph of a function is a picture of the function’s ordered pairs. f(x) is not “f times x” or “f multiplied by x.” f(x) means “the value of f at x.” So f(1) represents the value of f at x =1 Caution

Example 1A: 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 = ƒ(–2) = Use the graph to find the corresponding y-value for each x-value. ƒ(0) = ƒ = ƒ(–2) =

In the notation ƒ(x), ƒ is the name of the function In the notation ƒ(x), ƒ is the name of the function. The output ƒ(x) of a function is called the dependent variable because it depends on the input value of the function. The input x is called the independent variable.

Example 2a Graphing Functions Graph the function. 3 5 7 9 2 6 10 Do we connect the points? Graph the function f(x) = 3x – 1. Make a table. f(x) = 3x – 1 (x, f(x)) f(-1) = (3(– 1) – 1 f(0) = 3(0) – 1 f(1) = 3(1) – 1

Example 3A: Entertainment Application A carnival charges a $5 entrance fee and $2 per ride. Write a function to represent the total cost after taking a certain number of rides. ALWAYS DEFINE: r = number of rides, C = total cost in dollars. First, identify the independent and dependent variables. Cost depends on the entrance fee plus the number of rides taken Dependent variable Independent variable Cost = entrance fee + 2 × number of rides taken C(r) = 5 + 2r Replace the words with expressions. What is the value of the function for an input of 12, and what does it represent?

Check It Out! Example 3a 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. What is the value of the function for an input of 24, and what does it represent?