Identify Functions

Front

What is a function in mathematics?

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 relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What does it mean if a relation is 'not a function'?

Back

If a relation is 'not a function', it means that at least one input is associated with more than one output.

Front

Given the pairs (6,-5), (7,-3), (8,-1), (9,1), is this a function?

Back

Yes, this is a function because each x-value is unique.

Front

Given the pairs (9,5), (10,5), (9,-5), (10,-5), is this a function?

Back

No, this is not a function because the x-values 9 and 10 are associated with multiple y-values.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input corresponds to 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 is associated with two different outputs.