Identifying Functions

Front

What is a function?

Back

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

Front

How can you identify a function from a set of ordered pairs?

Back

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

Front

What is the vertical line test?

Back

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.

Front

Is the relation {(1, 2), (2, 3), (1, 4)} a function? Why?

Back

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

Front

Is the relation {(3, 5), (4, 6), (3, 7)} a function? Why?

Back

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

Front

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

Back

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

Front

What is a linear function?

Back

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

Front

What is a quadratic function?

Back

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

Front

What is the domain of a function?

Back

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