Need help with continuous piecewise functions

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kristoball

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Mar 27, 2012
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Hello, I'm having some problems with getting started on piecewise functions and other continuous functions, so could someone show me how to start and where to go to find the answer for a few examples?

Ex. #1: g(x) = x2-c2 if x<5 and g(x) = cx+19 if x ≥ 5. Find the two values of the constant c for which the function g(x) would be continuous.

Ex. #2: Consider the piecewise-defined function f(x) = 4x2+8 if x < -1, f(x) = Ax+B if -1 ≤ x < 3 and f(x) = 12x if x ≥ 3. Given that f is continuous everywhere, determine the values of A and B.

I just don't know how to even begin setting up the problem to solve any part of it. I would appreciate any help. Thanks!
 
kristoball said:
Hello, I'm having some problems with getting started on piecewise functions and other continuous functions, so could someone show me how to start and where to go to find the answer for a few examples?
Ex. #1: g(x) = x2-c2 if x<5 and g(x) = cx+19 if x ≥ 5. Find the two values of the constant c for which the function g(x) would be continuous.
Click to expand...
Solve 25 -\(\displaystyle c^2\)=5c+19
 
Kristoball, what pka is trying to say is that for a piecewise function to be continuous, then the values of the functions must be equal at the value where the graph changes from one function to another. In this case at x=5. If they are not the same, then there will be a discontinuity in the form of a "jump" discontinuity.

Hope this makes sense.
 
Thanks guys, that makes sense. What do I do to start the second example now?

Thanks!
 
kristoball said:
Thanks guys, that makes sense. What do I do to start the second example now?

Thanks!
Click to expand...

Apply the same concept that we mentioned above, but now you have to do it for x = -1 and x = 3. Give it a shot and let us know if you have any problems.
 
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