Classification of Discontinuities: Summary
Read this topicProblems 17
- Which function(s) above is/are continuous?
- The above graph has one discontinuity and is of the following function: f(x)={−5x−5−2x<58x≥5f(x) = \begin{cases} -\frac{5}{x-5}-2 & x <5 \\ 8 & x \ge 5 \end{cases}f(x)={−x−55−2…
- Select the intervals on which the graph is continuous.
- True or False: 1x\frac1xx1 has an infinite discontinuity.
- Which of the following graphs is continuous?
- Consider the following graph. What type of discontinuity is the graph representing?
- Consider the following graph. What type of discontinuity is represented?
- Which of the following represent discontinuous functions of time? Select all that apply.
- The following graph is an example of what type of discontinuity?
- Which of the following lists of data points cannot come from a continuous function over the reals?
- What kind of discontinuity is at x=2x=2x=2 for the function f(x)=1(x−2)2f(x)=\dfrac{1}{(x-2)^2}f(x)=(x−2)21?
- What kind of discontinuity is at x=2x=2x=2 for the function f(x)={2−x2x<212xx≥2f(x)=\begin{cases}2-x^2&x<2\\\frac1{2x}&x\ge2\end{cases}f(x)={2−x22x1x<2x≥2?
- What kind of discontinuity is at x=2x=2x=2 for the function f(x)={1x2−2x≠20.5x=2f(x)=\begin{cases}\frac{1}{x^2-2}&x\ne2\\0.5&x=2\end{cases}f(x)={x2−210.5x=2x=2?
- What kind of discontinuity does this graph have? f(x)=1x+1x2f(x)=\frac1x+\frac1{x^2}f(x)=x1+x21
- What kind of discontinuity does this graph have? f(x)={3x+8x<12−4xx≥1f(x)=\begin{cases} 3x+8&x<1\\ 2-4x&x\geq1 \end{cases}f(x)={3x+82−4xx<1x≥1
- What kind of discontinuity does this graph have? f(x)={3x+8x≠12−4xx=1f(x)=\begin{cases} 3x+8&x\ne1\\ 2-4x&x=1 \end{cases}f(x)={3x+82−4xx=1x=1
- While it is not clear in the picture, you may assume the function is equal to 0 at x=0x=0x=0. Noting this, which of the following discontinuities does the function above have?