Consider the function

MATHEMATICS · Multi correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

f(x)=\begin{cases}x-[x]-\frac12,&\text{if }x\notin I\\0,&\text{if }x\in I\end{cases}

, where

[\cdot]

denotes the greatest integer function and

I

is the set of integers. For

-2\le x\le2

, let

g(x)=\max\{x^2,f(x),|x|\}

. Which of the following pieces are part of the definition of

g(x)

? (1)

g(x)=x^2

-2\le x\le-1

(2)

g(x)=1-x

-1<x\le-\frac14

(3)

g(x)=\frac12+x

-\frac14<x<0

(4)

g(x)=1+x

0\le x<1