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asnaseer Group TitleBest ResponseYou've already chosen the best response.1
have you attempted to sketch the curve first?
 one year ago

FutureMathProfessor Group TitleBest ResponseYou've already chosen the best response.0
dw:1375034315072:dw
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
which part are you stuck on?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
how do i sketch if i dont know the points
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
all i see are x+1, x <> 2 then im stuck
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i can't use calculator.
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
ok  lets break it down into smaller steps
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
first, you are told that:\[f(x)=x+1\]if \(x\le2\) agreed?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so lets sketch this...
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so for a) since it;s coming from the left side it must be negative... and we use the top function, correct?
 one year ago

FutureMathProfessor Group TitleBest ResponseYou've already chosen the best response.0
Its already been sketched btw
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375034583963:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ok how did you sketch that ? :(
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I just sketched y=x+1 got 2 points on it: when x=0, y=1 when x=2, y=3 and then just drew a line
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
we are told that this is only for x less than or equal to 2. so we need to CHOP the curve at x=2 and draw a filledin dot at that point. it needs to be filledin because it INCLUDES the value at x=2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so the actual line should look like this:
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
does that make sense?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ohhhhh okay :)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375034970995:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so when are the times that we fill in the dots?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
and don't fill in?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
you always fillin the dots if the point INCLUDES the value  so all these would result in filling in the dot:\[x\le2\]\[x=2\]\[x\ge2\]and all these would NOT be filledin:\[x<2\]\[x>2\]
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
note that the first 3 INCLUDE the point x=2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
if that makes sense, then we can move onto the next part...
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yes :)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so stoping at two we fill in
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
and whatever is greater than 2 we leave alone?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i got it..
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
ok, so 2nd part of the curve is defined as:\[f(x)=1\]if \(x\gt2\) agreed?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so first lets sketch f(x) = 1
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375035727853:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
wait, can't we sketch x=3 because it says x is GREATER than 2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
now here we are told that this part is only valid for \(x\gt2\), so we need to draw a circle (not filledin) at the point x=2 and throw away everything to the left of this point
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375035852984:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yeah but wait, im not sure why we are using 1 when we can use 3 since it says x>2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the value of f(x) = 1 for x greater than 2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
that includes points such as x=2.000001, x=2.5, x=3, x=99, etc
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
i.e. ALL points to the right of (and NOT including) x=2
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375035980350:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh okay so i can use 3.. great
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so now we just combine both parts of the curve to get...
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375036030210:dw
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
make sense?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375036145535:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
got it
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
good. now we can examine the lmits
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ok :)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the 1st one is limit as x tends to 2 from the negative side
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
so  look at the curves and see what you think the answer should be for this case
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375036264164:dw
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
1 zt 2^
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
why is it 1 and not 1?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i see it's coming from the left side and the answer is going to be negative.
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
why is it going to be negative?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
but where do i look, in the y?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
because it's coming from the left?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
lets approach the limit in steps
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
how do i look for the limit when it approaches to 2?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375036393036:dw
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1375036417600:dw
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
can you see now what the limit should be as x approaches 2 from the lefthandside?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so its 3?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
perfect! well done! :)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
now try to do the same for x approaching 2 from the righthandside
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
right side of 2 it approaches at 1
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
bingo! you're a pro now! :)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
2 is undefined?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
the /tricky/ part now is what is the limit as x approaches 2 (without being told whether its from the left or right side)?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I believe you have grokked this now! :)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
because, it's not coming from either side.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
omg thank you!!!! :))
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
thank you so much!!
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
yw  I'm glad I was to explain it well enough for you to understand. :)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i'll apply this to the rest when im doing a problem
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
perfect!  keep at it  you seem to have a natural ability at this. :)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
What if they tell us to calculate instead of sketching?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
do we simply substitute?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
@asnaseer
 one year ago
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