Identifying 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

How can you determine if a relation is a function?

Back

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

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, it is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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 the set of points {(1,2), (1,3)}, where the input 1 has two different outputs.

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 (x-values).

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 (y-values).

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 f(x) = mx + b.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.