algebra 2 problem

Question

I have this problem how would this be answered

f(x) = piecewise

[x+3 if-2,

x<1 9 if x=1

-x+2 if x>1 ]

 

what would be the

domain, function and intercept ?

Answer 1

x-intercepts (where f(x)=0)

x+3=0 for x<1

x=−3 .Check condition: −3<1 true

9=0 at x=1 No solution.

−x+2=0 for x>1

x=2 2>1 true

x-intercepts are:

(−3,0) and (2,0)

y-intercept where x=0

Since 0<1, use the first rule: f(0)=0+3=3 y-intercept: (0,3)

So, domain : (- ∞, + ∞), x-intercepts: (−3,0), (2,0)​ y-intercept: (0,3)​