4. Function Notation notes.notebook 1 November 10, 2014 Function Notation
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4. Function Notation notes.notebook
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Function Notation
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Warm Up
1. 5x – 2 when x = 4
4. 2 – t2 when
3. when x = 16
94
18
48
5. Give the domain and range for this relation: {(1, 1), (–1, 1), (2, 4), (–2, 4), (–3, 9), (3, 9)}.
D: {–3, –2, –1, 1, 2, 3} R: {1, 4, 9}
Evaluate.
2. 3x2 + 4x – 1 when x = 5
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Write functions using function notation.
Evaluate and graph functions.
Objectives
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Some sets of ordered pairs can be described by using
an equation. When the set of ordered pairs described by
an equation satisfies the definition of a function, the
equation can be written in function notation.
Function Notation
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Function Notation
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ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3
Output value Output value Input valueInput value
ƒ of x equals 5 times x plus 3. ƒ of 1 equals 5 times 1 plus 3.
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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 + 3 (x, y) (x, 5x + 3)
ƒ(x) = 5x + 3 (x, ƒ(x)) (x, 5x + 3)Notice that y = ƒ(x) for each x.
The graph of a function is a picture of the function’s ordered pairs.
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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
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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) =
ƒ = 8 + 4 =
ƒ(–2) = 8 + 4(–2) =
,
ƒ(0) = 8 + 4(0) = 8
ƒ = 8 + 4 = 10
ƒ(–2) = 8 + 4(–2) = 0
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Evaluating Functions
• Given f(x) = 4x + 8, find
• f(2)
= 4(2) + 8= 16
f(2)f(2)
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Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
Use the graph to find the corresponding yvalue for each xvalue.
ƒ(0) = 3
ƒ = 0
ƒ(–2) = 4
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Determine the value of x when given f(x).
• Given f(x) = 4x + 8, determine x when:
f(x) = 2
f(x) = 1
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Example 2A: Graphing FunctionsGraph 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.
x 3x – 1 f(x)
– 1 3(– 1) – 1 – 4
0 3(0) – 1 – 1
1 3(1) – 1 2
Graph the points.
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