Draw examples of functions which are continuous and piecewise continuous, or which have di erent kinds of discontinuities. As to the original question, I'll leave that up to you. A function is piecewise continuous on 0 1) if f(t) is piecewise continuous on 0 N for all N>0. So, the answer to "which of the functions corresponding to these three plots is continuous?" can be either "none" or "all" depending on the fine points of your definition of continuity. Under these definitions, all three of your plotted functions would be continuous. However, there are other definitions of continuity, whereby a function is also continuous at $x_0$ if either one-sided limit exists, and the function is undefined on the other side. We can also determine the differentiability class of a piecewise continuous function. This won't happen in any of your functions at $x_0=\pi$. It turns out to be a well-behaved, non-piecewise function. This is because in order for a limit $\displaystyle$ to exist, the function must be defined in some open interval containing $x_0$. Nevertheless, your question opens up a point I think is important to address.īy your definition of continuity, none of your plotted functions are continuous. As such, each of the functions is defined on all of $\mathbb R$. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100) Learn more.
To graph the linear function, we can use two points to connect the line. For all intervals of x other than when it is equal to 0, f (x) 2x (which is a linear function). Using the graph, determine its domain and range. It tracks your skill level as you tackle progressively more difficult questions. Graph the piecewise function shown below. You're failing to account for the fact that $f_1$, $f_2$, $f_3$ all have periods of $2\pi$. IXLs SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. For problems 3 7 using only Properties 1 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points.
0 kommentar(er)
