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# 5 4 continuity-ofa_function

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### 5 4 continuity-ofa_function

1. 1. Continuity of a Function
2. 2. <ul><li>A function is continuous if you can draw it without lifting your pen from the paper. </li></ul>
3. 3. <ul><li>A function is continuous at a point x = a if </li></ul><ul><li>f ( a ) is defined </li></ul><ul><li>exists and </li></ul>
4. 4. <ul><li>Some Important Continuous Functions </li></ul><ul><li>All polynomial functions </li></ul><ul><li>Rational functions, as long as the denominator is nonzero </li></ul><ul><li>The sum, difference, product, and quotient (as long as the denominator is nonzero) of two continuous functions </li></ul>
5. 5. <ul><li>2.a Determine whether each function is continuous or discontinuous. If discontinuous, state where it is discontinuous. </li></ul>