Determine if there is a value for c which makes the function continuous on R2.

h(x,y) = {c + y, if x less/equal 3
{ 5-x, x3

Question

Determine if there is a value for c which makes the function continuous on R2.

h(x,y) = {c + y, if x less/equal 3
{ 5-x, x>3

anonymous · Answer

The way to think about these is to realize that if the function is going to be continuous, it must provide the same result for either rule... so (c+y)  must be equal to (5-x) at that x=3 point where the rule shifts.

anonymous · Answer

Except the way this function is written, I'm not sure that's the best approach.  I'll think about it for a bit...

anonymous · Answer

but since 5-x can't equal 3, theres no value of c that would make it continuous?

anonymous · Answer

maybe... at x less than 3, the function value doesn't even depend on values of x.

At x greater than 3, the function value doesn't depend on y

anonymous · Answer

I think this is like a horizontal line on one side and a vertical line on the other.  Weird problem

anonymous · Answer

hmmm .. soo thinking no value that makes it continuous?

anonymous · Answer

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anonymous · Answer

That's what I'm thinking, but I'm still a bit confused by it.  Sorry, seemed easy at first glance, and got more weird as I re-read it.

anonymous · Answer

so .. would (3,5) be the value? possibly ... i guess, hmm

anonymous · Answer

Oh aack... I got that drawing all backward :(

anonymous · Answer

Good news is I got myself unconfused... hang on, I'll draw it again. :)

anonymous · Answer

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