Mathematics Functions and Graphs

These flashcards cover essential vocabulary related to functions, relations, equations, and their graphical representations in mathematics.

Function

A relation where each x has only one y.

Relation

A set of ordered pairs (anything that pairs x with y).

Domain

All x-values the function can take.

Codomain

The set of possible y-values.

Range

The y-values that actually happen.

One-to-one function

Every x has one y AND every y has one x.

Onto function

All values in the codomain are used.

Bijective function

Both one-to-one and onto.

Slope formula

m = (y2 - y1) / (x2 - x1)

Slope-Intercept Form

y = mx + b where m is the slope and b is the y-intercept.

Vertical asymptote

Graph blows up, indicating a discontinuity.

Jump discontinuity

Graph jumps to a new height.

Piecewise function

A function made of different formulas depending on x-values.

Horizontal line test

If a horizontal line hits the graph more than once, then it's NOT one-to-one.

Absolute value inequality

An inequality involving absolute value, requiring case splits.

Complex number

A number in the form a + bi where i = √(-1).

Conjugate

For a complex number a + bi, its conjugate is a - bi.

System of equations

A set of equations with the same variables, needing to be solved simultaneously.

Vertical shift

A transformation that moves a graph up or down.

Horizontal shift

A transformation that moves a graph right or left.

Rigid transformation

Transformation that keeps the shape of a graph the same.

Non-rigid transformation

Transformation that alters the shape of a graph (stretched/compressed).