# Discontinuous function

Define a discontinuous function and state the conditions for discontinuity.

Find whether the following functions are discontinuous: f(x)=1/x and f(x)=(x)^(1/2)

Solve the following:(involves jump discontinuity)

A tomato wholesaler finds that the price of newly harvested tomatoes is $16 per pound if he purchases fewer than 100 pounds each day. However, if he purchases at least 100 pounds daily, the price drops to $14 per pound. Find the total cost function.

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#### Solution Preview

Definition of Discontinuous function:

If the function is not continuous at c then is said to be discontinuous at c.

Note that is discontinuous at if one (or more) of the three conditions given in the definition for continuity fails to hold.

Conditions for Discontinuity:

f is discontinuous at under any of the following ...

#### Solution Summary

This shows how to determine if functions are discontinuous and solves a problem using jump discontinuity.