Understanding 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 does it mean for a relation to pass the vertical line test?

Back

A relation passes the vertical line test if no vertical line intersects the graph of the relation more than once, indicating that each input has only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for every value of x, there is a unique value of f(x).

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 {(1, 2), (1, 3)}, because the input '1' is associated with two different outputs.

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 which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a set of points represents a function?

Back

You can determine if a set of points represents a function by checking if any x-value is repeated with different y-values.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically 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.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the function; it represents how much y changes for a unit change in x.