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# PC 1 continuity notes

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### Transcript

• 1. Precalculus<br />Continuity, End Behavior<br />A continuous function:<br />Types of discontinuity:<br />Continuity test:<br />A function is continuous at x = c if it satisfies the following conditions:<br />
• The function is ______________________ at c. ________________ exists.
• 4. The function approaches the same y value on the ________________________________ sides of x = c.
• 5. The y value that the function approaches is from each side is __________________.
Is the function continues at the given x-value?<br />a)fx=3x2+7; x = 1<br />b)fx=x-2x2-4; x = 2<br />c)fx=1x if x>1x if x≤1; x = 1<br />Increasing, Decreasing, End behavior<br />Describe the end behavior of the functions. Give the intervals on which they are increasing or decreasing.<br />a)fx=-2x3b)gx=-x2-x+5<br />______________________________________________ are the points on a graph at which a line drawn tangent to the curve is horizontal or vertical.<br />
• ___________________________________ is where the function changes from increasing to decreasing.
• 6. ___________________________________ is where the function changes from decreasing to increasing.
• 7. _____________________________________________ is where the graph changes its curvature.
Rational Functions<br />A rational function is the __________________________________ of two polynomial functions.<br />Rational functions have _______________________________________________________.<br />
• This creates either a ___________________________________________ or a ________________ in the graph.