# Properties of Continuous Functions

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1.Show that a polynomial function is continuous at every point of R.

2. Show that a rational function (a quotient of two polynomial functions) at every point where it is defined.

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#### Solution Preview

Please see the attachment.

1. Show that a polynomial function is continuous at every point of R.

We use the following properties of continuous functions to prove the fact.

I. If f(x) and g(x) are continuous functions at a point x=a, then (f+g)(x) is continuous at x=a and also f(x).g(x) is continuous at x=a

Using this, we can see that f(x)=xn is ...

#### Solution Summary

This solution uses the following properties of continuous functions to prove the fact.

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