Algebra 2 Honors: 1.1-1.5

Function

1. Relationship between input (x) and output (y) values

2. Every input has exactly one output

3. X-values cannot repeat

4. Vertical line test

Domain

X-values

Range

Y-values

Codomain

1. Set of all y-values

2. Assumed to be all real numbers unless otherwise states

One-to-one function

1. Every y-value is paired exactly with one x-value

2. Y-values cannot repeat

3. Horizontal line test

Onto function

Codomain equals the range

Continuous

Graphed with a line or unbroken curve

Discrete

Function where points are not connected

Two types of sets

1. Infinite

2. Finite

Set notation

1. Roster notation; written with {}

2. Set-builder notation; written with {}

3. Interval notation

   1. [] = include, filled in dot

   2. () = exclude, empty dot

Linear functions

1. No variable raised to a power above one

2. Can be written in f(x)=mx+b

3. Can be written in standard form (Ax+By=C)

   1. A is positive; A, B, and C are neither fractions or decimals

Intercepts

1. X-intercepts

   1. Intercepts x-axis and y=0

2. Y-intercepts

   1. Intercepts y-axis and x=0

Symmetry

1. Line symmetry

   1. Even function

   2. f(-x) = f(x)

2. Point symmetry

   1. Odd function

   2. f(-x) = -f(x)

Extrema

Minimum and maximum values

End behavior

Behavior of a graph as x approaches positive or negative infinity

HOYVUX

1. Horizontal

2. O = slope

3. Y = number

4. Vertical

5. Undefined slope

6. X = number

Inequality rules

1. Dotted line = < or >

2. Solid line = ≤ or ≥

3. Shading

   1. If > or ≥, shade above or right if vertical

   2. If < or ≤, shade below or left if vertical