TITLE: Intervals and plotting functions
QUESTION [3 upvotes]: I am having a problem with this task. I am asked to plot two functions:
$f_1(x)=\dfrac{x^2-7}{x+\sqrt{7}}$
and 
$f_2(x)=\dfrac{x^2-7}{x+2.645751311}$
and i am asked to plot these functions with x in the interval [-2.6458 .. -2.6457] and describe what i am seeing. I get this output:
I don't have enough reputation to post images but i get these outputs for function 1 and 2:
http://i.stack.imgur.com/14xN6.png
http://i.stack.imgur.com/PjQ04.png
What am i supposed to be seeing? I see that $f_1$ seems pretty normal but $f_2$ seems to do a wierd cross.

REPLY [1 votes]: The plots are correct. Note that the function $f_1$ can be transformed: $$f_1(x)=\dfrac{x^2-7}{x+\sqrt{7}} = \dfrac{(x-\sqrt7)(x+\sqrt7)}{x+\sqrt{7}} = x-\sqrt7$$
Hence here the limit for $x \to -\sqrt7$ is well defined for $f_1$. For $f_2$ this does not work, even though $2.645751311$ is very close to $\sqrt7$. This explains the "broken" graph for $f_2$.
{"set_name": "stack_exchange", "score": 3, "question_id": 1434818}