For the first question I want an example, then I need to see if I understand.
Question 1: Describe a situation that represents inverse variation.
Question 2: When does a discontinuity result in a vertical asymptote? When does it result in a hole in the graph?
Bonus question: Is the vertical asymptote the one on the X axis or Y axis?
1. Inverse variation
Let the price of bananas = P and the quantity = Q (in pounds )
Then, the quantity we buy will be greater when the price decreases and less when the price increases
This can be modeled by the function
Q = k / P where k is the variation constant
Discontinuity resulting in a vertical asymptote at x = 5 ⇒ f(x) = 1 / ( x - 5 )
[Occurs when the denominator of a rational function cannot be "factored out " ]
Discontinuity that results in a "hole" at x = 5 ⇒ f(x) = ( x^2 - 25) / (x - 5)
[Occurs when the denominator of a rational function can be "factored out " ]
A vertical asymptote goes through the x axis and is parallel to the y axis