1. 7.4 Function Notation and Linear Functions

2. Objective 1
Use function notation.
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3. 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)
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4. 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:
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5. f (–3) f (t) Let Find the following. CLASSROOM EXAMPLE 2
Evaluating a Function
Let Find the following.
f (–3) f (t)
Solution:
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6. 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:
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7. 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
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8. 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
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9. 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).
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10. 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:
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11. 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:
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12. Graph linear and constant functions.
Objective 2
Graph linear and constant functions.
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13. 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 (−∞, ∞).
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14. 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}
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