How to find the value of a and b that makes the following function continuous at x = 2

Question

f(x) = 4x + a if x > 2, 6 if x = 2, bx + 4 if x < 2

Answer 1

To be continuous, you want the f(x) value to be the same for all three increments surrounding x = 2. To do that, since f(2) = 6, you can set each of the other two portions of the function equal to 6:

4(2) + a = 6

8 + a = 6

a = -2

b(2) + 4 = 6

2b = 2

b = 1

So for f(x) to be continuous, "a" must be -2 and "b" must be 1