Unit 1 Pre-Calculus Vocabulary

domain

set of all input values of a function.

range

set of all output values of a function.

Vertical Line Test (VLT)

a test used to determine if a graph is a function; the vertical line test will only touch the graph once if it is a function

decreasing function

occurs when there is a positive change in x creates a negative change in y or f(x) value

increasing function

occurs when there is a positive change in x creates a positive change in the y or f(x) value

continuous function

every value in the domain has a corresponding output value

constant function

occurs when there is a positive change in x creates a change of zero in the y or f(x) value

removable Discontinuity

a point on the graph that is undefined or does not have a value. It creates a gap in the graph

jump Discontinuity

has two different limits as you approach a point

infinite Discontinuity

occurs when one side of the function has a limit of infinity

unbounded

no value a or b that is above or below all other values

local minimum

the lowest y value of a function, multiple of these

local maximum

the highest y value of a function, multiple

absolute minimum

smallest value of the entire function, ONLY one

absolute maximum

largest value of the entire function, ONLY one

even function

symmetrical about the y-axis, proved by showing that f(x) = f(-x)

odd function

rotational symmetry about the origin, proved by showing that f(-x) = -f(x)

horizontal asymptote

the line y=b, such that it shows the limit as x → -∞ and x → ∞

vertical asymptote

the line x=a, as the graph approaches the limit or the y value goes to -∞ or ∞

function

A relationship between two variables such that each input has exactly one output.