Chapter 4.7, Problem 14PPS

To determine

To Graph and Find:

Graph the function and state the domain and range.

Answer to Problem 14PPS

Domain is all real numbers.

Range is all integral multiples of 0.5 .

Explanation of Solution

Given Information:

Given equation is :

  $y=h(x)=\frac{1}{2}〚x〛+1$

Concept Used :

Step Function:

The graph of a step function is a series of line segments .Because each part of a step function is linear , this type of function is called a piecewise-linear function.

One example of a step function is the

Greatest Interger Function, written as $f(x)=〚x〛$ , where f(x) is the greatest integer not greater than x . For example , $〚6.8〛=6$ because 6 is the greatest integer that is not greater than 6.8 .

Greatest Integer Function:

Parent Function : $f(x)=〚x〛$

Type of Graph : disjointed line segments

Domain : All real numbers

Range : All integers

Graph :

  

Calculation:

Make a table of values for :

  $h(x)=\frac{1}{2}〚x〛+1$

x	$\frac{1}{2}〚x〛$	$h(x)=\frac{1}{2}〚x〛+1$
0	0	1
0.5	0	1
1	0.5	1.5
1.5	0.5	1.5
2	1	2
2.5	1	2
3	1.5	2.5

Now, plotting the values of x and h(x) , we get our graph

  

For the domain, wee see x- coordinate values. Because the dots and circles overlap , the domain is all real numbers .

For range, we see y -coordinate values. So, the range is all integral multiples of 0.5 .