# Thread: Value of the constant c: continutity question

1. ## Value of the constant c: continutity question

For what value of the constant is the function continuous on where

f(y)= (y^2) - c if y E (-inf,5)
cy + 5 if y E [5,inf)

i have no idea where to even start on this. for some reason i think its going to be a simple one. maybe not.

could i get some help please.

thank you

2. Look att the function when y=5. What do have to hold for f(y) to be continous when y=5?

3. Originally Posted by mybrohshi5
For what value of the constant is the function continuous on where

f(y)= (y^2) - c if y E (-inf,5)
cy + 5 if y E [5,inf)

i have no idea where to even start on this. for some reason i think its going to be a simple one. maybe not.

could i get some help please.

thank you

Since this function is piecewise, and we know that it is continuous everywhere except possibly at y=5, we must analyze this point.

To ensure continuity at y=5, All we must do is make

$\displaystyle \lim_{y\to5^-}f(y)=\lim_{y\to5^+}f(y)$

So, we write

$\displaystyle \lim_{y\to5^-}(y^2-c)=\lim_{y\to5^+}(cy+5)$

Can you finish?

4. No i guess i cant finish it. i understand why you set the limits equal to each other but i guess i cant figure out how to get an exact value for c?

thank you for the help

5. Originally Posted by mybrohshi5
No i guess i cant finish it. i understand why you set the limits equal to each other but i guess i cant figure out how to get an exact value for c?

thank you for the help
It's easy my friend! Solve for c!

implies that $\displaystyle y^2-c=cy+5$

So, all you gotta do is solve the system.

6. thank you. i tried that earlier after you posted the first time but could not solve for c.
i got it now though. im not having a great math morning lol

thank you again