Increasing and Decreasing Intervals
In this lesson on increasing and decreasing intervals, the concept of what it means for a function to be increasing or decreasing is explained, with a focus on supply and demand functions. The difference between strictly increasing and increasing, as well as strictly decreasing and decreasing, is also discussed. The lesson then moves on to discuss how to determine whether a function is increasing or decreasing algebraically, with examples given for linear, quadratic, exponential, and logistic functions. Finally, it is explained that the vertex of a quadratic function determines whether it is increasing or decreasing.
Understand what the terms increasing and decreasing mean with regards to a relationship. In particular, be clear on how demand and supply relationships work (i.e. are they increasing or decreasing, strictly or over only parts of the domain).
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- Notes - Notes from this lesson.
- Problem Set - A problem set from this lesson.
- Problem Set Solutions - Solutions to the problem set for this lesson.
- Definition of Increasing / Decreasing 1 - A definition of the term "increasing function"
- Definition of Increasing / Decreasing 2 - Calculus definition of a function increasing or decreasing on an interval
- Definition of Increasing / Decreasing 3 - Definition of a Monotonic function
- Supply and Demand 1 - Explanation of supply and demand and how it works.
- Supply and Demand 2 - Another explanation of supply and demand.
- Supply and Demand 3 - A definition of the term "market price"
- What are some characteristics of supply and demand functions?
- What are increasing and decreasing functions and intervals?
- What are supply and demand functions?
- What is the definition of an increasing or decreasing function?
- What is a monotonic function?
- What does it mean for a function to be strictly increasing or strictly decreasing?
- How can you tell where a function is increasing or decreasing from a table of values?
- How can you tell if an exponential or logistic function is increasing or decreasing from functional notation?
- What is a constant function?
- Why are exponential and logistic functions either always increasing or always decreasing?
- Where does a quadratic function go from increasing to decreasing or vice versa?
- How can you tell where a quadratic function is increasing or decreasing from functional notation?
- How can you tell where a function is increasing, decreasing, or constant from a graph?
- Why are demand functions always decreasing?
- Why are supply functions always increasing?
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Staff Review
This lesson explains increasing and decreasing functions and intervals and uses some of the most famous functions of this type: supply and demand curves. All terms and definitions are discussed and explained in the many web / document resources for this lesson. This is a very useful and helpful lesson for learning about increasing and decreasing functions.
