Identifying Functions

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

A set of ordered pairs is a function if no x-value is repeated with a different y-value.

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

No, because the x-value 1 has two different y-values (2 and 4).

No, because the x-value 3 has two different y-values (5 and 7).

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

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

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

A quadratic function is a function that can be expressed in the form y = ax² + bx + c, where a, b, and c are constants.

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