Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

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 with different second elements.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonproportional relationship?

Back

A nonproportional relationship is one where the ratio of the output to the input is not constant.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

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 is associated with exactly one output.

Front

What does it mean for a function to be proportional?

Back

A proportional function is one where the output is directly proportional to the input, often represented as y = kx, where k is a constant.

Front

How can you identify a function from a table of values?

Back

To identify a function from a table, check that each input (x-value) corresponds to only one output (y-value).