💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Find the numbers at which $f$ is discontinuous. At which of these numbers is $f$ continuous from the right, from the left, or neither? Sketch the graph of $f$.$f(x) = \left\{ \begin{array}{ll} 2^x & \mbox{if$ x \le 1 $}\\ 3 - x & \mbox{if$ 1 < x \le 4 $} \\ \sqrt{x} & \mbox{if$ x > 4 $} \end{array} \right.$

Limits

Derivatives

Discussion

You must be signed in to discuss.
Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp

Video Transcript

Okay, so here we have the piecewise defined function F of X to graph a piecewise defined function in dez mose you write down what the function is, for example, F of X equals two to the ex. But since uh that's the definition of uh ffx only when in this case X is less than or equal to one. You have to put uh those particular X values. That dysfunction is only defined for these X values. You have to put it in these little curly brackets, that's how you put this in decimus. So the blue curve here is F of X equals to two D X for X less than or equal to one. The green portion of the graph of F of X. F of X is defined to be three minus X when X is between one and four in case that's the green portion of the grave, last but not least. The purple portion of the graph of F of X F of X is defined to be the square root of X when X is strictly greater than four. So for X greater than for the purple graph represents f of X equals the square root of X. Now you can see that this function is continuous almost everywhere, except when X equals four, X equals X equals for um f of X is discontinuous. And that's because as X approaches for from the negative side, the function is approaching negative one. And as X approaches for from the positive side, F of X approaches to. So we have a dis continuity at X equal sport uh The function F of X is continuous uh From the left of four, and function is also continuous from the right of X equal sport.

Temple University

Topics

Limits

Derivatives

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp