2.3 Review: Properties of Functions

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

How do you determine if a function is even?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f.

Front

How do you determine if a function is odd?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f.

Front

What is a local maximum?

Back

A local maximum is a point in the domain of a function where the function value is greater than the values of the function at nearby points.

Front

What is a local minimum?

Back

A local minimum is a point in the domain of a function where the function value is less than the values of the function at nearby points.

Front

What is an absolute maximum?

Back

An absolute maximum is the highest point over the entire domain of a function.

Front

What is an absolute minimum?

Back

An absolute minimum is the lowest point over the entire domain of a function.

Front

What does it mean for a function to be neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd.

Front

How can you find the intervals where a function is increasing or decreasing?

Back

You can find intervals of increase or decrease by analyzing the first derivative of the function.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a function has a local maximum or minimum at a critical point.