Identifying Functions

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

Which set of ordered pairs is a function? {(9,5), (10,5), (9,-5), (10,-5)} or {(6,-5), (7,-3), (8,-1), (9,1)}?

Back

{(6,-5), (7,-3), (8,-1), (9,1)} is a function because each x-value is unique.

Front

What does it mean for a relation to NOT be a function?

Back

A relation is NOT a function if at least one input (x-value) has more than one output (y-value).

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is NOT a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a function?

Back

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

Front

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

Back

An example is {(1,2), (1,3)}, where the input 1 has two different outputs.

Front

What are inputs and outputs in a function?

Back

Inputs are the x-values, and outputs are the corresponding y-values in a function.

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 has only one output.

Front

What is the domain of a function?

Back

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