Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can name the three conditions that must all hold for a graph to be unbroken at x = c. (Guide: “What a discontinuity is”; Practice Q1, Q5(c))
- I can name the three types of discontinuity and state the limit evidence that defines each one. (Guide: “The three types you need”; Practice Q1)
- I can explain why a function can be discontinuous at c even when f(c) is defined. (Guide: Figure 1(a), Worked example 2; Practice Q1)
- I can explain why a jump cannot be fixed by changing one function value. (Guide: Worked example 2; Practice Q7(c))
Skills
- I can find and classify the discontinuities of a rational function by factoring and cancelling. (Guide: Worked example 1; Practice Q2, Q6)
- I can find the one-sided limits at the points where a piecewise function changes rule. (Guide: Worked example 2; Practice Q7)
- I can rewrite an absolute value on each side of c to detect a jump. (Guide: “Piecewise functions and absolute values”; Practice Q3)
- I can read one-sided limits and function values from a graph with holes, filled dots and asymptotes. (Guide: Figure 1; Practice Q5)
- I can say which type a table of values suggests. (Guide: “Tables of values”; Practice Q4)
Reasoning
- I can write a justification for each type using one-sided limits and f(c). (Guide: “Writing the justification”; Practice Q5(b), Q7(a))
- I can explain why a zero denominator does not always mean a vertical asymptote. (Guide: Worked example 1; Practice Q6(d), Q7(b))
- I can explain why a table suggests a type but does not justify it. (Guide: “Tables of values”; Practice Q4)
All ticked? Move on to Topic 1.11 with the Defining Continuity at a Point study guide, or return to the Calculus AB roadmap or the Calculus BC roadmap.