Functions - Bk 5 Chpt 8

Domain

Set of inputs or x values

Range

Set of outputs or y values

Codomain

Set of possible outputs

Ordered pairs

Coordinates

Relation

Set of ordered pairs. All functions are relations but not all relations are functions

Vertical line test

Function can only pass through a vertical line once (if more then it is not a function)

f: R → R: x → x² + 2

name: domain → codomain: input → rule (→ output → range)

gf(x)

g after f ie find f then put f into the x values of g

Injective function

one input for every output (can have empty outputs) crosses once on the horizontal line test

Surjective function

nothing is left unused (one output can have multiple inputs) crosses at least once on the horizontal line test

Bijective

Is both surjective and injective; has one output for every input without any unused outputs

Positive quadratic shape

U shape

Negative quadratic shape

N shape

Positive cubic shape

ends in U shape (up down up)

Negative cubic shape

ends in N shape (down up down)

Completing the square

1. half middle value
2. square result
3. take from last value

Plotting graphs

1. Find x and y values
2. Find turning point
3. Is it positive or negative

a.2²

passes through a on the y axis

x⁻²

downward sloping

x⁺²

upward sloping

large base eg 9³

steep slope

exponential graphs cut which axis

y

logarithmic graphs cut which axis

x

f(x) + 2

↑ 2

f(x) - 2

↓ 2

f(x+2)

← 2

f(x-2)

→ 2

\-f(x)

reflected in the x axis

3f(x) or f(x) = 3x(_)(_)

turning points increase up or down (going up continue up going down continue down) by 3

½f(x) or f(x) = ½x(_)(_)

turning points decrease up or down (going up go down and going down go up) by 2 (as ½ = -2)