Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has 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 more than once, it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every x-value is paired with only one y-value.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one corresponding y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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 x-value 1 is paired with two different y-values.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with an output.

Front

What does it mean if a mapping diagram shows an x-value with multiple y-values?

Back

If a mapping diagram shows an x-value with multiple y-values, it indicates that the relation is not a function.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each y-value is paired with exactly one x-value.