problem with sketching graph using limits

[avanm]

Hi there, I feel like I have no idea what im doing when I comes to sketching graphs using limits. Im fine with evaluating limits from graphs but not the other way around. In the attached files I show the graph I made but I think it is wrong. Can anyone show me how to make a proper graph that satisfies limits? Can one part of the function satisfy two conditions?

Thank you, I appreciate the help!

 

[Dr.Peterson]

Hi there, I feel like I have no idea what im doing when I comes to sketching graphs using limits. Im fine with evaluating limits from graphs but not the other way around. In the attached files I show the graph I made but I think it is wrong. Can anyone show me how to make a proper graph that satisfies limits? Can one part of the function satisfy two conditions?

The biggest problem I see is that what you drew is not a function. You'll have to have only one line in (-1, 0). Some of the limits are wrong, too, but many are good.

Beyond that, I suggest that you use you what said you can do, to find the various limits in your graph and check whether it fits! Most of it is fine; so just erase the bits that don't work and try again. Let us know where you see errors, and why you have trouble fixing them.

One of the things that make sketching a graph like this harder than reading a given graph is that there is a lot more freedom; you are not given enough information to be sure of many parts, so you have to make some arbitrary choices. Some choices may conflict with others, so just go back and try again.

But you clearly do have some idea what you are doing!

 

[avanm]

I see what you mean, does this one look better? I’m worried about the left hand side of the graph.

 

[Steven G]

I see what you mean, does this one look better? I’m worried about the left hand side of the graph.

Nicely done!