00:01
For this question, we're given the function f of x is equal to the piecewise defined function cx plus 9 for x is less than or equal to 2 and cx squared minus 7 for x is greater than 2.
00:21
And it says, what value of c? what does c equal if we want this function to be continuous? so if i look at each piece, that's a polynomial function, linear.
00:33
This is a polynomial function.
00:35
It's quadratic.
00:36
So everywhere in the piece, it is continuous.
00:40
So the only question is, what's happening at x equals 2? so if i find x equals 2, then this piece must match up to this piece.
00:53
Now, here it's defined at x equals 2.
00:55
So i can put in an x equals 2.
00:57
Technically, i should do the limit of the bottom one as x approaches 2 from the right.
01:04
However, i would evaluate that limit by doing the direct substitution.
01:08
So i'd be putting 2 in for x anyways.
01:10
All right, so let's just put in 2 for each x.
01:13
So the top piece is c times 2 for x plus 9.
01:17
That needs to equal c times 2 squared minus 7.
01:23
All right, so this is going to be 2c plus 9 equals 4c minus 7...