The variable is in the bottom of a fraction or in the denominator. (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner – as one value increases, the other decreases. For example, a biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker’s speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance.
Please start by addressing one or more of the following topics to get the discussion going:
- How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate.
- Pick a field of study of interest to you and give an example of variation in that field. Some possible areas to consider are: Economics, Finance, Geometry and Physics. Example: If your hourly pay rate is $15/hour, then your weekly pay p is given by the formula p=15h where h is the number of hours worked in a week. So, your weekly pay varies directly as the number of hours worked in a week with the constant of variation = 15.
- Most formulas are actually examples of variation. Pick a well-known formula and describe the type of variation as well as the constant of variation, k. Example: The area A of a triangle with base b and height h is given by the formula A=½bh. So, the area of a triangle varies jointly as the base and height (both direct) with the constant of variation = ½.
- Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book.