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Two questions

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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?

Feb 12, 2018

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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

2.

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   Feb 12, 2018
edited by CPhill  Feb 12, 2018