Relations, Functions, & Linear vs. Nonlinear

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-coordinate) and an output (y-coordinate).

Front

What is a function?

Back

A function is a special type of relation where each input (x-coordinate) is associated with exactly one output (y-coordinate).

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for a graph to be a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to locate a point on a coordinate plane, written as (x, y).

Front

What is the x-coordinate in an ordered pair?

Back

The x-coordinate is the first number in an ordered pair, representing the horizontal position on the coordinate plane.

Front

What is the y-coordinate in an ordered pair?

Back

The y-coordinate is the second number in an ordered pair, representing the vertical position on the coordinate plane.

Front

How do you determine if a set of points is a function?

Back

Check if any x-coordinate is repeated with a different y-coordinate; if so, it is not a function.

Front

What happens to y in the equation y = 2x if x is doubled?

Back

If x is doubled, y also doubles.