Let be the function defined by for

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

h

be the function defined by

h(x)=\lfloor x-1.5\rfloor

for

-2\le x\le 4

. Answer the following questions. (i) Draw the graph of

h

on the given domain, marking all jumps and closed/open end points. (ii) List all maximal intervals within

[-2,4]

on which

h

is constant. (iii) Write the domain of

h

. (iv) Write the range of

h

. (v) If

k(x)=h(x)+3

, determine the range of

k

. Explain your answer briefly.