For what value of 'a' is the following function continuous at every x? f(x)= x^2 - 117, x or equal to 13

Question

For what value of 'a' is the following function continuous at every x?
f(x)= x^2 - 117, x < 13
        2ax, x >or equal to 13

anonymous · Answer

since to the left and to the right of x=13, the function is continuous, you have to find a value for which x^2-117 is equal to 2ax,
plug 13 into both sides and solve
(13)^2 - 117 = 52
52 = 2a*13
52=26a
a=2

anonymous · Answer

thats fantastic!, so basically if the limit exists from the left and right I just have to plug in where their telling me its near and solve for x?

anonymous · Answer

Yeah, just imagine the graph of it, you can't control x^2-117, so the way I look at it is I try to aim the side I can modify so they connect.
You have it right, make it so that both sides equal each other at the point of the discontinuity

anonymous · Answer

now, if there was no limit say, to the right. would there be no answer?

anonymous · Answer

I'm not sure what you mean by no limit to the right. If you mean it goes to infinity, then yes there is no answer

anonymous · Answer

yea thats it. i appreciate the help!