Function notation

1. Day 2: Fnct notation, evaluating fnct, finding domain from equation
NOTATION
A function may be specified by a rule or an equation.
Notation:
(1) y = x2 + 1 y equals x squared plus one
(2) {(x, y) y = x2 + 1} set of all points (x, y) such that
y = x2 + 1
(3) f(x) = x2 + 1 f of x equals x squared plus one
(4) f: f(x) = x2 + 1 function f maps x to x2 + 1
f
(5) x x2 + 1 x gets mapped to x2 + 1 through
function f
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2. EVALUATING FUNCTIONS
Evaluation = Substitution
A: Evaluate x2 + 3x ­ 1
when x = ­ 2
B: If f (x) = x2 + 3x ­ 1,
evaluate f(­2)
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3. 1: Let f (x) = | 2 x + 1 | ­ x
Find...
a. f ( 0 ) =
0
b. f ( 1 ) =
1
c. f ( ­2 ) =
­2
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4. Sometimes a function is represented by a graph...
3: Given the graph of f(x)
y
Find
a. f (­3) =
b. f (4) =
x
c. f (x) = 3
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5. 4:
5:
6:
5

6. DOMAIN FROM EQUATION
Equation Rule Example
f﴾x﴿ = ­ 2x + 3
Linear f﴾x﴿ = mx + b
f﴾x﴿ = |x ­ 2| + 5
Absolute f﴾x﴿ = a|x ­h| + k
Value
f﴾x﴿ = 3﴾x + 2﴿2 ­ 4
f﴾x﴿ = ax2 + bx + c
Quadratic
f﴾x﴿ = a﴾x ­ h﴿2 + k
*Radical f﴾x﴿ = √stuff f﴾x﴿ = √x ­ 4
*Fractional 1 f(x) = 1
f(x) = x ­ 5
stuff
f(x) = 1
2x2 + 5x ­ 3
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