Functions, Functions, 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

What is the vertical line test?

Back

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

Front

What are the domain and range of a function?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Front

What does it mean if a function has a repeated x-value?

Back

If a function has a repeated x-value, it means that there are multiple outputs (y-values) for the same input (x-value), which violates the definition of a function.

Front

What is the range of a function?

Back

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

Front

How can you tell if a graph is a function?

Back

You can tell if a graph is a function by using the vertical line test. If any vertical line crosses the graph more than once, it is not a function.

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 is associated with two different outputs.

Front

What does it mean for a table to represent a function?

Back

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

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.