Functions (ordered pairs & tables)

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) where each input is related to exactly one output.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) where 'x' is the first element and 'y' is the second element, representing a point in a coordinate system.

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 set of ordered pairs represents a function?

Back

Check if any x-value is repeated; if it is, then y is not a function of x.

Front

What is a vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of x and y values, showing how y changes with respect to x.

Front

Give an example of a function using ordered pairs.

Back

Example: {(1, 2), (2, 3), (3, 4)} - Each x-value is unique.

Front

Give an example of a relation that is not a function using ordered pairs.

Back

Example: {(1, 2), (1, 3), (2, 4)} - The x-value '1' is associated with two different y-values.

Front

What is the domain of a function?

Back

The domain is the set of all possible x-values (inputs) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible y-values (outputs) that the function can produce.