Relations, Domains, and Ranges SOL1216

Front

What is the definition of a relation in mathematics?

Back

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

Front

What is the definition of a function?

Back

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

Front

How do you find the domain of a relation?

Back

The domain of a relation is the set of all possible input values (x) that can be used in the relation.

Front

What is the range of a relation?

Back

The range of a relation is the set of all possible output values (y) that result from the inputs in the domain.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

How can you determine if a relation is a function using a table of values?

Back

A relation is a function if no two ordered pairs have the same x-value with different y-values.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is the slope of a linear function?

Back

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

Front

What is an example of a non-function relation?

Back

An example is the relation {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function by checking if any vertical line intersects the graph at more than one point.