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one-to-one function

A function where each element of the range is paired with exactly one element of the domain.

onto function

Each element of the range corresponds to an element of the domain.

continuous relation

A relation that can be graphed with a line or smooth curve.

discrete relation

A relation in which the domain is a set of individual points.

VERTICAL LINE TEST

A line is a function is it passes the

standard form

A linear equation written in the form Ax+By=C, where A, B, and C are integers whose greatest common factor is 1, A ≥ 0, and A and B are not both zero.

slope

(y₂-y₁)/(x₂-x₁)

parallel lines

2 lines that never cross/intersect and stay the same distance apart

perpendicular

two lines that intersect and form a right angle are

family of graphs

A group of graphs that displays one or more similar characteristics.

y-intercept

the point where the line crosses the y-axis

x-intercept

the point where the line crosses the x-axis

Absolute Value Function

any f(x) = | x |

bivariate relation

Data with two variables.

correlation coefficient

If σ₁ and σ₂ are the variances of Y₁ and Y₂, the correlation coefficient is:

*dependent variable

The other variable in a function, usually y, whose values depend on x.

Dilation

a transformation that changes the size of an object, but not the shape

direct variation

If gummy bears cost $3.50 per pound, how much will 6 pounds cost? How much would a half a pound cost?

greatest integer function

A step function written as f(x)= [x], where f(x) is the greatest integer less than or equal to x.

independent variable

the tested varaible

Linear Equation

A polynomial equation of the first degree whose graph is a line.

Linear Function

y = mx + b

linear inequality

contains a single variable on either side of the inequality symbol.

line of fit

A line that closely approximates a set of data.

negative correlation

y tends to decrease, as x increases

Parent Function

the most basic function of a family of functions, or the original function before a transformation is applied

piecewise-defined function

A function that is written using two or more expressions.

point-slope form

Given a point (x₁, y₁) and slope m

positive correlation

y tends to increase, as x increases

prediction equation

An equation suggested by the points of a scatter plot that is used to predict other points.

Quadratic Function

a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero

Rate of change

A value that results from dividing the change in a function (y-values) of a variable by the change in the variable (x-values). It is another name for slope.

reflection

It is a transformation that flips a figure over a line of reflection.

regression line

predicts the value for the response variable y as a straight line function of the value x of the explanatory variable

Scatter plot

is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.

Slope-Intercept Form

a linear equation written in the form y = mx + b, where m represents slope and b represents the y-intercept

step function

A function whose graph is a series of line segments.

translation

It is a transformation that moves points the distance and in the same direction.