Properties of 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 domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) 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 (dependent variable) that result from using the function.

Front

How do you find the x-intercept of a function?

Back

To find the x-intercept, set the output (y) to zero and solve for the input (x).

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the output value at the second point is greater than the output value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the output value at the second point is less than the output value at the first point.

Front

What is a continuous function?

Back

A continuous function is a function that does not have any breaks, jumps, or holes in its graph.

Front

What is a discontinuous function?

Back

A discontinuous function is a function that has one or more points at which it is not continuous.

Front

What is a 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 a one-to-one function?

Back

A one-to-one function is a function where each output value is associated with exactly one input value, meaning no two different inputs produce the same output.