Mathematics

Problem

A function

g

is represented on the Cartesian plane by the following three pieces: (i)

y=(x+1)^2

for

-3\le x\le -1

(both endpoints are filled dots), (ii)

y=2

for

-1<x<2

(both endpoints are hollow dots), (iii)

y=1

for

x\ge 2

with a filled dot at

(2,1)

. What is the range of

g

? a)

(0,4]

[1,4]

[0,4]

[0,4)

Intuitive explanation

The range is the set of all $y$ -values the function actually outputs. You need to trace through each piece carefully, paying special attention to whether endpoints are included (filled dots) or excluded (hollow dots). For the parabola, find its minimum and maximum on the given interval; for the horizontal segments, just read off the $y$ -values that are actually attained. Then combine all three pieces to get the complete range.

Intuitive explanation

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