Key Features 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 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 function's value at the second point is greater than the 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 function's value at the second point is less than the value at the first point.

Front

What is end behavior of a function?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

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

Back

To find the x-intercepts, set the function equal to zero and solve for x.

Front

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

Back

To find the y-intercept, evaluate the function at x = 0.

Front

What is a maximum point of a function?

Back

A maximum point is a point on the graph of a function where the function value is greater than the values of the function at nearby points.

Front

What is a minimum point of a function?

Back

A minimum point is a point on the graph of a function where the function value is less than the values of the function at nearby points.

Front

What does it mean for a function to be positive?

Back

A function is positive on an interval if its values are greater than zero for all points in that interval.

Front

What does it mean for a function to be negative?

Back

A function is negative on an interval if its values are less than zero for all points in that interval.