Function or Not a Function

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 any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What defines 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 in the domain, there is one and only one corresponding y-value in the range.

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

How can you determine if a table represents a function?

Back

To determine if a table represents a function, check if any x-values are repeated. If an x-value appears more than once with different y-values, it is not a function.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a graph to be a function?

Back

For a graph to be a function, it must pass the vertical line test, meaning that no vertical line can intersect the graph at more than one point.

Front

What is an example of a non-function?

Back

An example of a non-function is the graph of a circle, as it fails the vertical line test by having multiple y-values for the same x-value.

Front

What is the domain of a function?

Back

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

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

How can you identify a function from a set of ordered pairs?

Back

To identify a function from a set of ordered pairs, ensure that no x-value is repeated with a different y-value. If all x-values are unique, it is a function.