Algebra Unit 4 Functions (notation & features)

domain

the set of all potential inputs (x-values)

range

the set of all potential outputs (y-values)

input

the x-value of a function (in the parenthesis for function notation); domain/independent variable

output

the y-value of a function (NOT in parenthesis for function notation); range/dependent variable

rate of change

use the slope formula (the vertical change divided by the horizontal change)

function notation

uses f(x) instead of y in the equation of a function

y-intercept

where x = 0 on the graph (vertical intercept)

x-intercept

where y = 0 on the graph (horizontal intercept)

relative minimum(s)

ALL dips/valleys (low points) on the graph (includes the absolute minimum)

relative maximum(s)

ALL peaks (high points) on the graph (can include the absolute maximum)

decreasing interval(s)

as the x-values increase, the y-values decrease; negative rate of change from left to right on the graph

increasing interval(s)

as the x-values increase, the y-values increase; positive rate of change from left to right on the graph

absolute maximum

corresponds to the highest point on the graph (if there are several peaks, this is the highest one)

absolute minimum

corresponds to the lowest point on the graph (if there are several valleys/dips, this is the lowest one)

interval notation

domain and range written using brackets and parenthesis

inequality notation

intervals written using inequality symbols