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    Continuity, Trends and Forecasting

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    1) What is a discontinuity? How are discontinuities found? Which types of graphs are continuous?

    3) If Bob starts off with a salary of $50,000 and earned $1000 a year for his salary, give the equation of his salary, S, for year t. Use this equation to find the year in which he would be earning $56,400. Show all your work using the equation.

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    Solution Preview

    From mathworld.com the definition of continuous is:

    A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological spaces form a category. The designation "continuous" is sometimes used to indicate membership in this category.

    This means that a function f(x) is continuous if its value approach f(a) as x approaches a

    Check out:

    In functions, we have three types of discontinuity:

    1. The function is not defined at a certain point.

    for example, look at the function:

    {2 x<0
    f(x) ={
    {2 x>0

    As you can see, the function has a value everywhere except at x=0 in which we don't know what ...

    Solution Summary

    Discontinuities, trends and forecasting are investigated in the following posting.