Functions and Relations

Front

What is a function?

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.

Tags

CCSS.8.F.A.1

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). Relations can be functions or not functions.

Tags

CCSS.8.F.A.1

Front

How can you determine if a mapping is a function?

Back

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

Tags

CCSS.8.F.A.1

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if each x-value is paired with exactly one y-value.

Tags

CCSS.8.F.A.1

Front

What is the vertical line test?

Back

The vertical line test is a method used 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

Give an example of a function using ordered pairs.

Back

Example: {(1, 2), (2, 3), (3, 4)} is a function because each x-value is unique.

Tags

CCSS.8.F.A.1

Front

Give an example of a relation that is not a function.

Back

Example: {(1, 2), (1, 3), (2, 4)} is not a function because the x-value '1' is paired with two different y-values.

Tags

CCSS.8.F.A.1

Front

What is an example of a function's domain and range?

Back

For the function f(x) = x^2, the domain is all real numbers, and the range is all non-negative real numbers.