Chapter 3.7, Problem 13PPS

To determine

To graph: the given function, to state the domain and range.

Explanation of Solution

Given information:

The function $g(x)=\frac{1}{2}[[x]]+1$

Concept used:

The greatest integer function produces the greatest integer less than or equal to the

Number.

Domain is the set of input values for which the function is defined.

Range is the set of output values for input values which are in domain.

Calculation:

Consider $g(x)=\frac{1}{2}[[x]]+1$

Make a table of values for $g(x)=\frac{1}{2}[[x]]+1$

$x$	$-1$	$-0.5$	$0$	$0.5$	$1$
$g(x)$	$0.5$	$0.5$	$1$	$1$	$1.5$

Graph:

The graph of $g(x)=\frac{1}{2}[[x]]+1$ is shown below.

Hence,

Domain is $(-\infty ,\infty )$ , Range is all integers $\{\mathrm{....}-1,-0.5,0,0.5,1,\mathrm{...}\}$ .