Functions

Front

What is a function in mathematics?

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

How can you determine if a graph represents a function?

Back

A graph represents a function if no vertical line intersects the graph at more than one point (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a curve is a graph of a function or not by checking if any vertical line crosses the graph more than once.

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

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; each input must correspond to exactly one output.

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 polynomial function of degree two, typically in the form f(x) = ax^2 + bx + c.

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.