Identify Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

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 relation to be a function?

Back

A relation is a function if every input has a unique output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

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

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 definition of a domain in a function?

Back

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

Front

What is the definition of a range in 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 if a function is linear?

Back

A linear function is a function that graphs to a straight line, typically in the form f(x) = mx + b.