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How would I graph an expression like
x^(2)1
I know I would first convert it to a piece wise function where:
 2 years ago
 2 years ago
How would I graph an expression like x^(2)1 I know I would first convert it to a piece wise function where:
 2 years ago
 2 years ago

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HermellaBest ResponseYou've already chosen the best response.0
WHOA 2 LAZY 2 ANSWER BOO HOO
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
x^(2)1 if x^(2) 1 >=0 and x^(2) + 1 x^(2) 1 <0
 2 years ago

HermellaBest ResponseYou've already chosen the best response.0
FIGURE IT OUTIT IS YOUR HW
 2 years ago

Callum29Best ResponseYou've already chosen the best response.0
Isn't it just the graph of x^2  1 but with the part which is below the xaxis inverted so that it is above the xaxis? You will lose differentiability at x=1 and x=1 but continuity is preserved so there is no need to define it piecewise?
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
So x^(2)1 if x^(2) 1 >=0 and x^(2) + 1 x^(2) 1 <0 x^(2)  1 if x >= 1 and x^(2) + 1 if x < 1 Thus I can just input values into both sides, anyone able to provide me with a more difficult piece wise function. I know it is elementary I just want to refresh my memory.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
@Hermella please don't yell at people to just figure it out on their own. They come on this site to get help. If you don't want to help, then just ignore their question.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
So how would you just graph x^21? this is a parabola right with yintercept 1 and xintercept 1 and 1
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
dw:1326156295808:dw
 2 years ago

Callum29Best ResponseYou've already chosen the best response.0
x^(2) + 1 if x < 1 violates x^(2) + 1 if x^(2) 1 <0. Take x = 1/2
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now what does x^2+1 look like (note we will worry about the domains in a sec)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
dw:1326156367729:dw
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now the first graph was for x>=1 so we need to play with's domain
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
dw:1326156439379:dw
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now for the 2nd part we have x<1
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
dw:1326156472771:dw
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
Oh thanks for going through this step by step, it is clear to me now. Could you give me an example of a piece wise function that is not continuous if not I understand
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
wait something is wrong with my graph its not all above the xaxis
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
ok so we had \[x^21=(x^21) \text{ if } x^21 \ge 0\] \[x^21=(x^21) \text{ if } x^21<0\] right?
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
don't understand what is incorrect with your graph it seems correct to me
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
\[(x1)(x+1) \ge 0 \] this is 0 when x=1 and x=1  1 1 now we need to test where (x1)(x+1) is greater than 0 so we try the first interval (inf,1) we choose a number like 2 (21)(2+1)=(3)(1)=3>0 so on the interval (inf,1)=> (x1)(x+1)>0 what about the interval (1,1) we choose a number like 0 (01)(0+1)=1(1)=1<0 so on this interval we have that (x1)(x+1)<0 now last interval (1,inf) we choose a number to try like 2 (21)(2+1)=1(3)=3>0 so for the interval (1,inf)=> (x1)(x+1)>0 so for this x^21=x^21 happens on (inf,1) and (1,inf) now lets check out the other equality x^21=(x^21)=x^2+1 this is for x^21<0 (x1)(x+1)<0 btw (1,1)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
i should have done all the work earlier i just skipped this algebra part
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
so do you understand x^21=x^21 on the intervals (inf,1), (1,inf) and x^21=(x^21) on the interval (1,1)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now back to our parabolas
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
so (1,1) does not exist in the domain?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
so x^21 we had dw:1326157039943:dw but we didn't have it for (1,1)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
so we actually have dw:1326157076390:dw
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
that is for the x^21=x^21 for the intervals (inf,1),(1,inf)
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
why is (1, 1) excluded from the domain I don't understand
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now for the middle part (1,1) we have x^21=(x^21)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
dw:1326157146780:dw
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
x^21=x^21 for x^21>0 right?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now did you solve x^21>0?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
you will get that x^21=x^21 is only true for the intervals (inf,1),(1,inf)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
now for x^21=(x^21) is only true for the intervals (1,1)
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
oh, because it is the only area of the graph that will make the graph less than zero
 2 years ago

myininayaBest ResponseYou've already chosen the best response.2
yes x^21<0 on the interval (1,1)
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
so when solving these it is important to make a chart and plug in numbers between the intervals
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
Thanks I think it is a bit more clear in my head how to solve these now I need to focus on the output of the piece wise function and use that to guide me on how to graph the function
 2 years ago

BlingBlongBest ResponseYou've already chosen the best response.1
after considering the graph of the various rules of the function
 2 years ago
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