Functions (ordered pairs & tables)

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane, where x is the horizontal value and y is the vertical value.

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 table represents y as a function of x?

Back

Check if each x-value in the table corresponds to only one y-value. If any x-value has multiple y-values, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, which can include functions but may also include pairs where an x-value corresponds to multiple y-values.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value corresponds to only one y-value.

Front

What is a domain in the context of functions?

Back

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

Front

What is a range in the context of functions?

Back

The range is the set of all possible output values (y-values) for a function.

Front

What does it mean for y to NOT be a function of x?

Back

It means that there exists at least one x-value that corresponds to more than one y-value.