1. continuous function

I keep getting confused on this problem. So it is:

determine a and b so that the following function is continuous on (-infinity, infinity)

f(x)= 3x-2, x is less than or equal to 4 and greater or equal to 2.

f(x)= x^2+ax+b, absolute value of (x-3) is greater or equal to 1.

2. 1) I'm pretty sure you have that first one a little backwards. Perhaps x <= 2 or x >= 4?

2) It will help to separate the definition, so I'll use

f(x) = 3x-2
g(x) = x^2 + ax + b

We'll just use g(x) when we are around x = 3 and g(x) when one (1) or more away.

Your task is to create a continuous function. The only trick is matching up the endpoints, since (thankfully) they are the same).

f(2) = 4
f(4) = 10

We must make g(2) = 4 and g(4) = 10

That's all. Let's see what you get.

3. got it!

ok i got it.

so

4+2a+b=4
2a+b=0

and

16+4a+b=10
4a+b=-6

a=-3
b=6

so if the x wasn't the same for both functions, then we couldn't solve this?

4. If the Domains don't match up rationally.

For example,

Find 'b' that makes this continuous.

f(x) = 3x - 5 for x < -10

g(x) = -3x + b for x > 4

It's silly. There's a giant gap!

5. oh i see.

do you tutor at a school or do private tutoring/know anyone in hawaii that helps calculus students??