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

J2easy said:
Really need help with this as I am so lost View attachment 36891
Click to expand...

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 [imath]\displaystyle{\lim_{x \rarr 0^+} f(x) = 3}[/imath] and [imath]\displaystyle{\lim_{x \rarr 0^-} f(x) = -2}[/imath]
Click to expand...

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 [imath]x = 0[/imath]. So you'll have a piecewise function (since the rules obviously have to change as [imath]x[/imath] passes [imath]0[/imath]), but those pieces can have any rule you like, as long as they head to the specified values of [imath]y[/imath].
 
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:

www.khanacademy.org

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

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
www.khanacademy.org www.khanacademy.org

(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.
 
You must log in or register to reply here.
Top