Question

need help with determining the intervals on which f is continuous

Answer 1

3-5, and 6 if you can help

Answer 2

#3- f is continuous at all points except x=2
#4- g is continuous at all points x greater than or equal to 2
#5- h is continuous at all points x greater than zero, as well as between -1<x<0. It is not continuous at 0, and it is not continuous at x<-1
#6) in order for something to be differentiable at the point, we need to first find the derivatives of both parts. so less than two is 3*a*x^2 and greater than 2 is 2*x. At 2, these have to be equal, so by setting them equal to eachother we have 3*a*(2)^2=2*2, so
a = 1/3
Then it also has to be continuous at that point. so for that, we plug a back into the original equation.
1/3*2^3=2^2+b.
b = 2/3