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 curve is a function. If a vertical line intersects the curve at more than one point, then it is not a function.

Front

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

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input).

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output).

Front

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

Back

Yes, this relation is a function because each input has exactly one output.

Front

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

Back

No, this relation is not a function because the input '1' has two different outputs (2 and 3).

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line.

Front

What is a quadratic function?

Back

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

Front

What is a constant function?

Back

A constant function is a function that always returns the same value regardless of the input.