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Continuity from PrecalculusA function is said to be continuous at c if its graph passes through the point at x = c without a “hole” or a “jump”.
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Continuity From CalculusA function f is continuous at c if the following three conditions hold:
Which Functions Are Continuous?
If functions f and g are continuous at c, then the following are also continuous at c:
All polynomial functions are continuous. Rational functions are not continuous when the denominator = 0 (vertical asymptote). Piece-wise functions have the potential to be continuous or not. |
Ex A: Determine if each function is continuous. If discontinuous, state why.
Ex B: Determine if each function is continuous. If discontinuous, state where it is discontinuous and why.
Assignment
Part A: Determine whether each function is continuous at c. If discontinuous, state why.
Part B: Determine whether each function is continuous. If discontinuous, state where it is discontinuous. (You’ve graphed some of these functions on previous homework.)
1.4 Notes & Homework
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1.4 Key
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