7.4 Function Notation and Linear Functions

Objective 1 Use function notation. Slide 7.4- 2

Use function notation. When a function f is defined with a rule or an equation using x and y for the independent and dependent variables, we say, “y is a function of x” to emphasize that y depends on x. We use the notation y = f (x), called function notation, to express this and read f (x) as “f of x.” y = f (x) = 9x – 5 Name of the function Defining expression Function value (or y-value) that corresponds to x Name of the independent variable (or value from the domain) Slide 7.4- 3

Let Find the value of the function f for x = −3. CLASSROOM EXAMPLE 1 Evaluating a Function Let Find the value of the function f for x = −3. Solution: Slide 7.4- 4

f (–3) f (t) Let Find the following. CLASSROOM EXAMPLE 2 Evaluating a Function Let Find the following. f (–3) f (t) Solution: Slide 7.4- 5

CLASSROOM EXAMPLE 3 Evaluating a Function Let g(x) = 5x – 1. Find and simplify g(m + 2). g(x) = 5x – 1 g(m + 2) = 5(m + 2) – 1 = 5m + 10 – 1 = 5m + 9 Solution: Slide 7.4- 6

CLASSROOM EXAMPLE 4 Evaluating Functions Find f (2) for each function. f = {(2, 6), (4, 2)} f (x) = – x2 f (2) = – 22 f (2) = – 4 Solution: x f(x) 2 6 4 f (2) = 6 Slide 7.4- 7

CLASSROOM EXAMPLE 5 Finding Function Values from a Graph Refer to the graph of the function. Find f (2). Find f (−2). For what value of x is f (x) = 0? Solution: f (2) = 1 f (−2) = 3 f (4) = 0 Slide 7.4- 8

Finding an Expression for f (x) Use function notation. Finding an Expression for f (x) Step 1 Solve the equation for y. Step 2 Replace y with f (x). Slide 7.4- 9

CLASSROOM EXAMPLE 6 Writing Equations Using Function Notation Rewrite the equation using function notation f (x). Then find f (1) and f (a). x2 – 4y = 3 Step 1 Solve for y. Solution: Slide 7.4- 10

Find f (1) and f (a). Step 2 Replace y with f (x). CLASSROOM EXAMPLE 6 Writing Equations Using Function Notation (cont’d) Find f (1) and f (a). Step 2 Replace y with f (x). Solution: Slide 7.4- 11

Graph linear and constant functions. Objective 2 Graph linear and constant functions. Slide 7.4- 12

Graph linear and constant functions. Linear Function A function that can be defined by f (x) = ax + b for real numbers a and b is a linear function. The value of a is the slope m of the graph of the function. The domain of any linear function is (−∞, ∞). Slide 7.4- 13

f (x) = −1.5 Graph the function. Give the domain and range. CLASSROOM EXAMPLE 7 Graphing Linear and Constant Functions Graph the function. Give the domain and range. f (x) = −1.5 Solution: Domain: (−∞, ∞) Range: {−1.5} Slide 7.4- 14