How do I approach this?

Question

anonymous · Answer

The function f is defined by: 
$$f(x)=\left\{ x^3+a : x \in(- \infty,0)\right\}$$
$$\left\{ x+b  :x \in [0,1) \right\} $$
$$\left\{ ax^2+b   :x \in (1,\infty) \right\}$$

where a, b are constants so that f is continuous everywhere. What are the possible values for 'a' and 'b'?

kainui · Answer

You want these to be continuous, which means exactly like what it sounds like. In order for that to happen you need the function to have an equal value at the points where it gets cut, which are at the points x=0 and x=1 on the domain. Just to give you a similar example, this is kind of what your'e looking at: |dw:1424583624543:dw| What you need to do is set them equal to each other at each point, so to start you out, you can join the first two by saying: $$\large x^3+a = x+b \text{    at x= 0 , so} \ \large 0^3+a = 0+b \ \large a=b$$ Now connect them up at the next point when x=1.

anonymous · Answer

I'm getting a & b=1. Is this correct?