I've been struggling with this problem for, I kid you not, a week off and on. I get part of it sketched but then I think I've contradicted myself and I start second guessing. I suppose I'll write what I think it says and correct me based on that.
I take this to mean that as x approaches y=2, we drop down to negative infinity. I've drawn a horizontal asymptote here but I'm unsure if that's correct.
As we get to negative 1 from the left, go north. This means we never actually hit -1 from the right, we just approach it infinitly right?
Does this mean from the other side we start drawing a line at point (-1,5) and go where? This is where after we go right a bit... This must join up to something else.
f is continuous from the right at -1
Does this information pairs up with the limit just above this one?
At this point I'm lost. I think I've messed something up before here and by the time I get to this point it's game over.
Second last piece of information.
Just draw an asymptote here right?
If time permits please show me how to appraoch this type of question. What should I look for first? What should I tackle last? I double checked all the equations, hopefully there are no typos.
To the far left, the graph approaches the horizontal line
There is a vertical asymptote at
As approaches -1 from the left, the graph rises to
As approaches -1 from the right, the graph approaches the point (-1,5).
As approaches 2 from the left, the graph goes down to
As approaches 2 from the right, the graph goes up to
As goes to infinity, the graph approaches the horizontal line
I believe the graph loioks like this . . .
Code:: | : *: | :* : | : * : | : * o | : * * : * | : * : | * : * - - - - - - - - - + - - +2 * : * : | * : * --------------------+-----+-------:--------*----------------- : | * : * : | : * : -2+ - - - : - - - - - - - - - - - - : | *: : | :
Well no wonder I got confused. I got the left one correct and the and centre one mostly correct but then the third one really screwed me up. I kept thinking the centre and right graphs were existing in the same x axis space (as in not a function, can draw a line through two lines). Thanks for the prompt answers.