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 graph represents a function?

Back

A graph that passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

Front

What is the vertical line test?

Back

A method to determine if a graph is a function; if a vertical line crosses the graph more than once, it is not a function.

Front

Identify the function from the following set of ordered pairs: {(1,2), (2,3), (1,4), (3,5)}

Back

The function is {(1,2), (2,3), (3,5)} because each input has only one output.

Front

What is an example of a non-function?

Back

A relation like {(1,2), (1,3), (2,4)} is not a function because the input '1' has two different outputs.

Front

If f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function means that each output is paired with exactly one input, so no two different inputs produce the same output.

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.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) that the function can produce.