f(x) = ax + 3 if x > 2,

f(x) = x + 5 if -2 <= x <= 2,

f(x) = 8x + b if x < -2

Find a + b if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).

Guest Jul 12, 2021

#2**+4 **

To find the value of a that makes the curve continuous at the upper intersection, set x = 2 in the upper two expressions and equate them:

i.e. a*(2) + 3 = (2) + 5

or 2a+3 = 7

a = 2

Similarly to find the value of b that makes the curve continuous at -2, set

(-2) + 5 = 8*(-2) + b

I'll let you finish.

Alan Jul 12, 2021