Help plotting maximum and minimum values on graph

Hello, I am going back to an unfinished homework assignment and I realized that I skipped this problem because my professor never covered it in class. (Doh) I could use your help with the following problem:

Sketch the graph of the function *f* that is continuous on [1,5] and has:

- absolute minimum at 2
- absolute maximum at 3
- local minimum at 4

I understand that the [1,5] means that I will be plotting points between 1 and 5 on the *x*-axis, and that the maxima/minima are basically *x* values, but how do I figure out what their *y* values are?

Thank you!

Danni

Re: Help plotting maximum and minimum values on graph

There is more than one such function, so your question should probably read "... the graph of a function ...".

You are correct that [1,5] means all x, $\displaystyle 1\le{x}\le5$. I would draw the graph by first drawing the minimum and maximum at x=2 and 3, then the minimum (with y value between the two others) at x=4, then connecting them and extending to the whole interval (staying between the minimum and maximum at x=2 and 3).

I think you have to just pick convenient y-values - there's not a single correct answer (unless there's some additional information you didn't put in your post).

- Hollywood

Re: Help plotting maximum and minimum values on graph

Hi dannibambi! :)

You can pick any y values you like, as long as they fit your criteria.

Your graph would for instance look something like this graph.