Question

Why is \[g(x)=1-x+|x|\] continuous?

Options

• Polynomial functions and \[|x|\] are continuous.

• \[g(x)\] is a quotient with denominator \[x\].

• \[|x|\] is continuous only when \[x\neq 0\].

• \[g(x)\] equals \[\tan x\].

Answer 1

The expression \[1-x\] is a polynomial function, and \[|x|\] is continuous. Their addition gives \[g(x)=1-x+|x|\], which is continuous.