Functions (Ordered Pairs & Tables)

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-value) with different second elements (y-values).

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 a set of ordered pairs to be 'not a function'?

Back

A set of ordered pairs is 'not a function' if at least one x-value is associated with more than one y-value.

Front

Given the set {(2,3), (2,4), (3,5)}, is this a function?

Back

No, because the x-value '2' is associated with two different y-values (3 and 4).

Front

What is the vertical line test?

Back

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

Front

Identify if the following set is a function: {(1,2), (2,3), (3,4)}

Back

Yes, this set is a function because each x-value is unique.

Front

Which of the following is a function? {(1,2), (1,3), (2,4)}, {(2,3), (3,4), (4,5)}

Back

The set {(2,3), (3,4), (4,5)} is a function because all x-values are unique.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, which can show how two quantities are related.

Front

If a function is represented as f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 4 + 3 = 7.