http://www.ck12.org Chapter 1. Functions and Graphs
Vocabulary
Increasingover an interval means to have a positive slope over that interval.
Decreasingover an interval means to have a negative slope over that interval.
Monotonicmeans that the function doesn’t switch between increasing and decreasing at any point.
Strictlyis an adjective that alters increasing and decreasing to exclude any flatness.
Guided Practice
- Estimate where the following function is increasing and decreasing.
- Estimate where the following function is increasing and decreasing.
- A continuous function has a global maximum at the point (3, 2), a global minimum at (5, -12) and has no relative
extrema or other places with a slope of zero. What are the increasing and decreasing intervals for this function?
Answers: - Increasing:x∈(−∞,− 1. 5 )∪( 1. 5 ,∞). Decreasing:x∈(− 1. 5 , 1. 5 )
- Increasingx∈(−∞,− 4 )∪(− 4 ,− 2. 7 )∪(− 1 , 2 )∪( 2 ,∞). Decreasingx∈(− 2. 7 ,− 1 )
- Increasingx∈(−∞, 3 )∪( 5 ,∞). Decreasingx∈( 3 , 5 )
Notice that the y coordinates are not used in the intervals. A common mistake is to want to use the y coordinates.
Practice
Use the graph below for 1-2.