A function is defined by these values... For which constants (a and b) is this function continuous? Where f(x) = x^3 for x

Question

A function is defined by these values... For which constants (a and b) is this function continuous?
Where f(x) = 
x^3 for x <-1
ax+b for -1 _<x <1
x^2+2 for x_>1

anonymous · Answer

So I would assume that $$\lim_{x \rightarrow 1-}$$ would be $$x^{3}$$

anonymous · Answer

and $$\lim_{x \rightarrow 1+}$$ would be $$x^{2}+2$$

anonymous · Answer

and $$\lim_{x \rightarrow 0-}$$ would be the same as $$\lim_{x \rightarrow 0+}$$ which would be ax+b. But where would I go next?

freckles · Answer

$$(-1)^3=a(-1)+b  \ a(1)+b=(1)^2+2$$
you have a system of equations to solve

freckles · Answer

I set left limit as x approaches -1 equal to right limit as x approaches -1
I set left limit as x approaches 1 equal to right limit as x approaches 1

freckles · Answer

you can simplify those equations so they don't look so junky

anonymous · Answer

Okay thank you so much, this is my second time taking this course and I have this condition where I keep getting sick, so I just wanted to say that I really appreciate the extra help. People like you keep me positive and working toward my goal

freckles · Answer

glad I could help