I am so confused on this question (calculus): Invent a function to satisfy lim_{x->0+} f(x) = 3 and....

[J2easy]

Really need help with this as I am so lost

 

[stapel]

Really need help with this as I am so lost View attachment 36891

Part of the text appears to be cut off. If the remaining text is not necessary, then it appears that the following is the exercise:

Invent a function, and sketch its graph, to satisfy $\displaystyle{\lim_{x \rarr 0^+} f(x) = 3}$ and $\displaystyle{\lim_{x \rarr 0^-} f(x) = -2}$

Note that the exercise asks you to "invent *a* function", rather than "find *the* function". This is because there are infinitely-many functions which will fulfill the requirement that the function has a break at $x = 0$. So you'll have a piecewise function (since the rules obviously have to change as $x$ passes $0$), but those pieces can have any rule you like, as long as they head to the specified values of $y$.

 

[khansaheb]

Really need help with this as I am so lost View attachment 36891

Can you sketch the function according to the "given" conditions ?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Dr.Peterson]

Did you try looking for examples of limits like these? Here are a couple pages with graphs similar to what you are expected to make:

One-sided limits from graphs (practice) | Khan Academy

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Limits (An Introduction)

(see the section "When it is different from different sides".)

It's unclear whether a graph alone will be enough, or whether you need to make up a piecewise definition of a function; in my mind, the former should be sufficient, because a graph defines a function. But at the least, these pages and others on the topic should help you understand the idea.

We could help a lot more if you showed all of the problem, and some little bit of thinking, so we could see where you need help.