Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is any set of ordered pairs.

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function?

Back

Use the Vertical Line Test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

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

What is the definition of ordered pairs?

Back

An ordered pair is a pair of numbers (x, y) where x is the first element and y is the second element.

Front

What is the output of the function g(x) = 2x + 5 when x = 4?

Back

g(4) = 2(4) + 5 = 13.

Front

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

Back

This is not a function because the input 1 has two different outputs (2 and 4).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

If a function is defined as f(x) = x^2, what is f(3)?

Back

f(3) = 3^2 = 9.