I'm stuck on this precalc question

Question

Give the multipart rule for g(x) for the following functions. g(x) = |f(x)|

(a) f(x) = −0.5x − 1

(b) f(x) = 2x − 5

(c) f(x) = x + 3

Answer 1

Remember lal=a when a≥0 and lal=-a when a<0.

(a) g(x)=l -0.5x-1 l

If -0.5x-1≥0, that is, x≤-2, then g(x)=-0.5x-1

If -0.5x-1<0 that is, x>-2, then g(x)=0.5x+1

(b) g(x)=l 2x-5 l

If 2x-5≥0, that is, x≥2.5, then g(x)=2x-5

If 2x-5<0 that is, x<2.5, then g(x)=-2x+5

(b) g(x)=l x+3 l

If x+3≥0, that is, x≥-3, then g(x)=x+3

If x+3<0 that is, x<-3, then g(x)=-x-3