Various Types of Graphs

In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. (Source: Wikipedia)

Detail Explanation of Various Types of Graphs

various types of graphs:

Line graphs: A line graph is the way of to representing the two pieces of information, which is usually related with respect to each other. This is more useful when comparisons are needed.



Pie Charts: A pie chart or (circle graphs) are normally used in showcasing a wholesome quantity; we have to show that how in this whole quantities are broken into parts.



Bar Charts: Bar chart is a type of chart, which has labeled horizontal or vertical bars showing a piece of information and an axis



Area Graphs are used to view the changes, how it get changed with respect to time. An area graph shows the contribution of to each data series in this form of a picture.




Another Type of the Problem for Various Types of Graphs


Coordinate type graph:

Plot the various types of graphs in this equation

1. y=x+6

2. y=x2

Solution

Problem 1: Make a graph with this equation

y =x+6

Substitute x=-2,-1, 0,1,2,3

x=-2 y= (-2)+6

By solving it we get

y=4

The ordered pair is (-2, 4)

x=-1 y= (-1)+6

By solving it we get

y=5

The ordered pair is (-1,5)

Similarly

x=0, we get y= 6

x=1, we get y=7

x=2, we get y=8

The co ordinate’s points are (-2,4),(-1,5),(0,6),(1,7), and (2,8)

Plot the table use this various coordinates

 

x	y
-2	4
-1	5
0	6
1	7
2	8

Problem 2: Make a graph with this equation

y =x2

Substitute x=-2,-1, 0,1,2,3

x=-2 y= (-2)2

By solving it we get

y=4

The ordered pair is (-2, 4)

x=-1 y= (-1)2

By solving it we get

y=1

The ordered pair is (-1,1)

Similarly

x=0, we get y= 0

x=1, we get y=1

x=2, we get y=4

The co ordinate’s points are (-2,4),(-1,1),(0,0),(1,1), and (2,4)

Plot the table use this various coordinates

x	y
-2	4
-1	1
0	0
1	1
2	4

Plot the graph for this various tables

Cube Root Formula

In math, a cube root of a value, represents `root(3)(x)` or x1/3, is a value a such that a3 = x. In general the cube root formula is defined as a value x are the numbers y which satisfy the following formula. By using this formula we can solve the cube root problems. Let, see some of the examples of cube root. This article very much helpful to you to solve the problem about the cube root. The cube root problem is used on many places and it is one of the basic mathematical operation.

Examples of Cube Root Formula:

All real numbers contains perfectly one real cube root and a duo of complex conjugate roots, and every nonzero complex values contains three distinct complex cube roots.

Example problem1:

Find the cube root of 8.

Solution:

The given problem can be written as: `root(3)(8)=2` since `2*2*2=2^3=8.`

Example problem2:

Find the cube root of 1.

Solution:

The given problem can be written as: `root(3)(1)=1` since `1*1*1=1^3=1.`

Example problem3:

Find the cube root of 27.

Solution:

The given problem can be written as: `root(3)(27)=3` since `3*3*3=3^3=27.`

Example problem4:

Find the cube root of -8.

Solution:

The given problem can be written as: `root(3)(-8)=-2` since `-2xx-2xx-2=-2^3=-8.`

Example problem5:

Find the cube root of -792.

Solution:

The given problem can be written as: `root(3)(-792)=-9.25213002`

Since, `-9.25213002xx-9.25213002xx-9.25213002=-9.25213002^3=-792.`

Practice Problems of Cube Root Formula:

Problem 1:

Find the cub root of 81.

Solution:

4.32674871

Problem 2:

Find the cub root of 100.

Solution:

4.64158883

Problem 3:

Find the cub root of 125.

Solution:

5

Problem 4:

Find the cub root of 343.

Solution:

7

Problem 5:

Find the cub root of 1000.

Solution:

10

Percentage to Grade Conversion

The percentage of the number is a method of showing the number with the denominator 100 as fraction. The percentage of the number is represented by the symbol “%” or “pct”. Percentage shows the relation of the two quantities, the first quantity is associated with the second quantity. So, first quantity should be larger than zero

Grades are the measurements which are standardized for understanding the academic level of the students. Percentage and its grades are listed below.

Percentage to Grade Conversion Table

Percent to grade point table
Percent	Grade points	Letter grade
0.1	0	F
0.25	0	F
0.26	0	F
0.27	0	F
0.28	0	F
0.29	0	F
0.3	0	F
0.31	0	F
0.32	0	F
0.33	0	F
0.34	0	F
0.35	0	F
0.36	0	F
0.37	0	F
0.38	0	F
0.39	0	F
0.4	0	F
0.41	0	F
0.42	0	F
0.43	0	F
0.44	0.1	F
0.45	0.2	F
0.46	0.3	F
0.47	0.4	F
0.48	0.5	F
0.49	0.6	F
0.5	0.7	D-
0.51	0.8	D-
0.52	0.9	D
0.53	1	D
0.54	1.1	D
0.55	1.2	D+
0.56	1.3	D+
0.57	1.4	D+
0.58	1.5	C-
0.59	1.6	C-
0.6	1.7	C-
0.61	1.8	C-
0.62	1.9	C
0.63	2	C
0.64	2.1	C
0.65	2.2	C+
0.66	2.3	C+
0.67	2.3	C+
0.68	2.4	C+
0.69	2.4	C+
0.7	2.5	B-
0.71	2.5	B-
0.72	2.6	B-
0.73	2.6	B-
0.74	2.7	B-
0.75	2.7	B-
0.76	2.8	B-
0.77	2.8	B-
0.78	2.9	B
0.79	2.9	B
0.8	3	B
0.81	3	B
0.82	3.1	B
0.83	3.1	B
0.84	3.2	B+
0.85	3.2	B+
0.86	3.3	B+
0.87	3.3	B+
0.88	3.4	B+
0.89	3.4	B+
0.9	3.5	A-
0.91	3.5	A-
0.92	3.6	A-
0.93	3.6	A-
0.94	3.7	A-
0.95	3.7	A-
0.96	3.8	A-
0.97	3.8	A-
0.98	3.9	A
0.99	3.9	A
1	4	A

Example to Percentage to Grade Conversion:

Example 1:

John scored the marks in five subjects 87, 90, 88, 76 and 65. The test is conducted for 100 marks in each subject. Find the grade of the john.

Solution:

Total marks of the test = 5 `xx ` 100 = 500

Total marks of the john = 87 + 90 + 88 + 76 + 65 = 406

Percentage of the marks scored by john = `406/500` `xx` 100 = 81.2% or `81.2/100` = .812

Therefore john got B grade


Example 2:

Martin scored the marks in five subjects 85, 95, 65, 75 and 55. The test is conducted for 100 marks in each subject. Find the grade of the Martin.

Solution:

Total marks of the test = 5 `xx` 100 = 500

Total marks of the Martin = 85 + 95 + 65 + 75 + 55 = 375

Percentage of the marks scored by Martin = `375/500` `xx` 100 = 75% or `75/100` = .75

Therefore Martin got B- grade

Practice Problems to Percentage to Grade Conversion:

Problem 1:

Paul scored the marks in five subjects 85, 98, 58, 67 and 94. The test is conducted for 100 marks in each subject. Find the grade of the Paul.

Solution is, Paul got B grade

Problem 2:

Steve scored the marks in five subjects 76, 86, 96, 66 and 56. The test is conducted for 100 marks in each subject. Find the grade of the Steve.

Solution is, Steve got B- grade

Inverse Cosine Graph

Inverse cosine  is one of the essential  inverse trigonometric function . Its principal values and range is
cos ^-1 : {(y,x)l y = cos x , x `in [ 0, pi]` , y `in` [-1,1]}


In this we deals with determining inverse tangent graphs.

Function	Domain	Principal Value (Range)
y =cos -1 x	R	[ 0, `pi`]

The graph of cos^-1 x is as follows :

. 

Inverse Cosine Graph : Examples

Example  1 : Draw the inverse cosine graph for the function

                                        y = cos^-1 ( x + 4 ) 

Solution : As it is given   y= cos ^-1 ( x + 4 ) so, there is a horizontal shift in the graph of   y = cos^-1 x by 4 units leftwards 

Graph as shown :

                  

Example  2  : Draw the inverse cosine graph for the function

                                       y = cos^-1 ( x ) - 3 

Solution : As it is given   y = cos^-1 ( x ) - 3

It can also be wirtten as  y + 3  = cos^-1 ( x ) so , there is a vertical shift in the graph of   y =cos ^-1 x by 3 unit downwards

Graph as shown :

                    

Example  3  : Draw the inverse cosine graph for the function

                                        y = cos^-1 ( x + 2 ) and   y = cos^-1 ( x - 1 ) on the same graph 

Solution : As it is given   y = cos^-1 ( x + 2 ) so, there is a horizontal shift in the graph of   y = cos^-1 x by 2 units leftwards and

               for  y = cos ^-1 ( x - 1 ) there is a horizontal shift in the graph of   y = cos^-1 x by 1 unit rightwards

Graph as shown :

             

Inverse Cosine Graph : Practice Problems

Problem 1  :  Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 5 )
Problem  2 :  Draw the inverse cosine graph for the function               
                                             y = cos^-1 ( x ) + 6
Problem  3  :  Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 1) and   y = cos^-1 ( x - 7 ) on the same graph

Number Line Estimation

In mathematics, a line with points marked on it is termed as number line. Every point represents a number in number line. This number line is mainly used for representing the numbers. From online, we have a clear description of number line estimation. This article gives the explanation of number line estimation and some example problems using number line.

Explanation to Number Line Estimation:

The facts of number line is as follows.

• A straight horizontal line with points that are evenly spaced.
• A number o is at center and positive numbers are at right side of 0 while the negative numbers are at left side of 0.
• The number line makes easy the arithmetic operations addition and subtraction.

A number line with points is as follows.

Let us see some example problems using number line.

Example Problems to Number Line Estimation:

Example: 1

Estimate a number 5 between the numbers 0 to 8.

Solution:

The estimation of a number 5 is as follows.

Example: 2

Estimate a negative number - 5 between -9 to 0.

Solution:

The estimation of a negative number -5 is as follows.

Example: 3

Add the numbers 1 and 6 using number line.

Solution:

Given: 1 + 6

Step 1:

Mark 1 on number line.

Step 2:

Start count and move from 1 at right side.

Step 3:

Stop count when it reaches 6 and mark the resultant value.

Answer: 7

Example: 4

Subtract 2 from 4 using number line.

Solution:

Given: 4 - 2

Step 1:

Mark a number 4 on number line.

Step 2:

Start count and move from 4 at left side.

Step 3:

Stop count when it reaches 2 and mark the resultant value.

Answer: 2

Practice Problems to Number Line Estimation:

Problem: 1

Add the numbers 2 and 6 using number line.

Answer: 8

Problem: 2

Subtract 3 from 4 using number line.

Answer: 1