Graphing-How Do you do it (1 Viewer)

[replayee]

SAy for example "graph y=xe^-x", would you guys find the derivative get the turning points etc etc. or would you just do wat my teacher tells us to do by going "as x approaches 0 from above y approaches infinity" and things as x approaches asymptotes etc????

 

[Riviet]

SAy for example "graph y=xe^-x", would you guys find the derivative get the turning points etc etc. or would you just do wat my teacher tells us to do by going "as x approaches 0 from above y approaches infinity" and things as x approaches asymptotes etc????

It depends on how much the detail the question wants, ie how many marks are awarded for your sketch. At 4 unit level, only use calculus if asked to find critical points or as a last resort since there are many other techniques that you have learnt that are more useful in helping you sketch the curve. Applying limits such as for as x->a, y->b, are useful to determine the behaviour of the curve in a certain area of the graph.

 

[sasquatch]

first i would draw y = x, and then y = e^-x. From this it would be possible to determine various parts of the graph, i.e. when it is negative or postive, where its cuts the y-axis, and show you where the graph is undefined.
From these two graphs you could multiply ordinates to determine the shape of the graph. You could also find turning points, if required, but i find just drawing the graph sufficient enough.

 

[Rax]

Yeah drawing graphs is where I tend to fall out, I can't even picture some graphs so it doesnt help at all. That and we havent even done half the the types of graphs in class ( ie inverse graphs)
But from what I have seen around this forum most people view calculus as a last resort or if the question specifies
GG