   Chapter 11.1, Problem 7ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Sketch a graph for each of the functions defined in 6—9 below. 7. h ( x ) = ⌈ x ⌉ − ⌊ x ⌋ for each real number x

To determine

Graph each of the function defined in 69 below.

h(x)=xx for all real numbers x.

Explanation

Given information:

Consider the function.

For all real numbers

h(x)=xx

The objective is to graph this function.

Concept used:

Calculation:

The objective is to graph this function.

Let x be a real number.

A floor function of x is denoted by f(x)=x and is defined by the greatest integer that is less than or equal to x.

A ceiling function of x is denoted by f(x)=x and is defined by the smallest integer that is greater than or equal to x.

The function h(x)=xx is the difference of ceiling function and floor function.

Now, examine the function h(x) for the small interval x(0,1).

0.5=1 and 0.5=0h(0.5)=0.50.5=10=1

Now, examine the function h(x) for the small interval x(1,0).

0.5=1 and 0.5=1h(0.5)=0.50.5=0(1)=1

Next, examine the function h(x) for integer value.

x=1

1=1 and 1=1h(1)=11=1(1)=0

Next, examine the function h(x) for integer value.

x=11=1 and 1=1h(1)=11=1(1)=0

Define a step function h(x) as below

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