Help with graphs! (1 Viewer)

[tohriffic]

How would I graph y = 2^{-sin x}?

Please go through what's in your mind cause I haven't a clue on how to sketch it. > <

I would really appreciate your help!

Thanks in advance.

 

[AAEldar]

Well, we know that is a periodic function that repeats every so that will indicate that this will repeat. How would I graph this? Table of values.









So, using that we can put those in the function.









Using that, we can sketch it!

But put the values of on the -axis instead.

 

[tohriffic]

Was hoping there was some shortcut... > ^ <

Thanks so much AAEldar (especially for the swift reply)!

 

[D94]

1) Sketch two graphs: (this is actually your question) and

2) For the critical points on , find where the corresponding values are on the graph.

3) Sketch.

It can work with any question, whether log or inverse or an expression raised to an expression etc.

 

[AAEldar]

Was hoping there was some shortcut... > ^ <

Thanks so much AAEldar (especially for the swift reply)!

Well that is pretty quick to do by hand (on the computer though it's longer to type out...).

No worries though

 

[tohriffic]

1) Sketch two graphs: (this is actually your question) and

2) For the critical points on , find where the corresponding values are on the graph.

3) Sketch.

It can work with any question, whether log or inverse or an expression raised to an expression etc.

I drew them both and then I got stuck... hurhur.. but cool, I'll remember your point about critical points.

Thanks D94.

 

[D94]

I drew them both and then I got stuck... hurhur.. but cool, I'll remember your point about critical points.

Thanks D94.

No worries. When I was first taught this method, I was stuck like you, but with practice, it's very easy to draw graphs. Essentially, my method is pretty much what AAEldar has, but I guess what I wrote is a generic method. Good luck

 

[lolcakes52]

All i can recommend is trying to get familiar with all types of graphs, this way you will notice trends such as how it is a periodic function (As AAElder pointed out), that the graph will have a minimum when -sin(x) has a minimum and a maximum when -sin(x) does and that it will never be equal to zero. That is really all you need to know to be able to graph it, basically find the minimum and maximum and make the rest up. Remember to put in intercepts and all that jazz though.

 

[math man]

A fast method is to appraoch it like this.... y=- sinx exists between -1 and 1 and now all exponentials are > 0 for all x and as the max value is 1 the max value on the composite graph will be 2^1=2....now when -sinx = 0 that will become 1 on the composite and when -sinx = -1 that will become 1/2...so basically the graph shifts up to 2 and starts from 1/2....so you just have the same -sinx graph from 1/2 to 2...

 

[tohriffic]

All i can recommend is trying to get familiar with all types of graphs, this way you will notice trends such as how it is a periodic function (As AAElder pointed out), that the graph will have a minimum when -sin(x) has a minimum and a maximum when -sin(x) does and that it will never be equal to zero. That is really all you need to know to be able to graph it, basically find the minimum and maximum and make the rest up. Remember to put in intercepts and all that jazz though.

Oh okay that makes sense. I like your point about the minimum and the maximum, I never really noticed it -slow- Haha well that is why I am doing these graphs So I can try and get familiar with them.

Thanks lolcakes.

 

[tohriffic]

A fast method is to appraoch it like this.... y=- sinx exists between -1 and 1 and now all exponentials are > 0 for all x and as the max value is 1 the max value on the composite graph will be 2^1=2....now when -sinx = 0 that will become 1 on the composite and when -sinx = -1 that will become 1/2...so basically the graph shifts up to 2 and starts from 1/2....so you just have the same -sinx graph from 1/2 to 2...

Oh okay, my graph sorta resembles a -sin x graph but it somehow looks a little different. Is this also like the table of values method? o:

And ty~

 

[math man]

Oh okay, my graph sorta resembles a -sin x graph but it somehow looks a little different. Is this also like the table of values method? o:

And ty~

it is sort of table of values...but you dont actually write it down...its all just a mental process