Is This a Function?

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a relation is a function using a table?

Back

A relation is a function if each x-value in the table corresponds to only one y-value.

Front

What does it mean if a graph fails the vertical line test?

Back

If a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the vertical line test?

Back

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

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 corresponds to only one y-value.

Front

What is an example of a function?

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)}.

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)} because the x-value 1 has two different y-values.

Front

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

Back

A one-to-one function is a function where each x-value corresponds to a unique y-value and each y-value corresponds to a unique x-value.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, and it determines the corresponding y-value (output).

Front

What does it mean for a function to be defined?

Back

A function is defined when there is a clear rule that assigns each input exactly one output.