Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I've answered an exercise on Stewart's Essential Calculus, he asks me to sketch a graph of an example of a function $f$ that satisfies all of the given conditions below:

  • $\lim_{x\rightarrow 3^+}f(x)=4$

  • $\lim_{x\rightarrow 3^-}f(x)=2$

  • $\lim_{x\rightarrow -2}f(x)=2$

  • $f(3)=3$

  • $f(-2)=1$

The plot below is the right answer. In my answer, the line that is passing through $a$ is passing through point $b$. Is my answer acceptable? I can't feel the guarantee that the line is really passing through point $a$ and I'm thinking that both answers are right.

enter image description here

share|improve this question
2  
How do you get the third condition, $\lim_{x\to-2}f(x)=3$, if your graph goes smoothly through $B=(-2,1)$? –  Rahul Oct 25 '12 at 11:41
3  
And if the limit from both sides is $3$, shouldn't it go through the point $P = (-2, 3)$ (instead of $A$ or $B$)? –  TMM Oct 25 '12 at 11:58
2  
What is the point $E$ doing there? $f(3)=4\ne3$. –  Gerry Myerson Oct 25 '12 at 12:07
1  
I just want to point out, you say "the plot below is the right answer" where it should say the plot below is a right answer, as it may not be unique. So your answer can be good, as long as it respect every conditions. –  Jean-Sébastien Oct 26 '12 at 15:11
1  
It may not pass through $a$ but if you pass through $b$ then you won't have condition $3$ respected. The function wants to go to $2$ at $-2$ coming from the left, but it just can't get there as it needs to be $1$ –  Jean-Sébastien Oct 26 '12 at 15:21

1 Answer 1

up vote 1 down vote accepted

Yes, basically right.

The slopes and convexity of the function may vary, but the main thing is that the graph of $f$ (what you called 'line') indeed wants to pass through $A$ (in a neighborhood of $x=-2$), but instead, at least at $x=-2$, it is 'sporadicly' valuated according to $B$. Similarly well plotted for $C,D,E$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.