Graphs and charts are visuals that show relationships between data and are intended to display the data in a way that is easy to understand and remember. People often use graphs and charts to demonstrate trends, patterns and relationships between sets of data.

Graphs are used in everyday life, from the local newspaper to the magazine stand. It is one of those skills that you simply cannot do without. Whatever your need or calculation, if used correctly, a graph can help you and make your life simpler. A graph can help you keep track of things and to be on top of your game.

Charts are used in situations where a simple table won’t adequately demonstrate important relationships or patterns between data points. When making your chart, think about the specific information that you want your data to support, or the outcome that you want to achieve .

Graphs are a common method to visually illustrate relationships in the data. The purpose of a graph is to present data that are too numerous or complicated to be described adequately in the text and in less space. If the data shows pronounced trends or reveals relations between variables, a graph should be used.

Three types of graphs are used in this course: line graphs, pie graphs, and bar graphs. Each is discussed below.

Charts present information in the form of graphs, diagrams or tables. Graphs show the mathematical relationship between sets of data. Graphs are one type of chart, but not the only type of chart; in other words, all graphs are charts, but not all charts are graphs.

There are several different types of charts and graphs. The four most common are probably line graphs, bar graphs and histograms, pie charts, and Cartesian graphs.

Advantages

• show each data category in a frequency distribution.
• display relative numbers or proportions of multiple categories.
• summarize a large data set in visual form.
• clarify trends better than do tables.
• estimate key values at a glance.
• permit a visual check of the accuracy and reasonableness of calculations.

Advantages: summarize a large dataset in visual form; easily compare two or three data sets; better clarify trends than do tables; estimate key values at a glance. Disadvantages: require additional written or verbal explanation; can be easily manipulated to give false impressions.

Graphs and charts provide major benefits. First, they can quickly provide information related to trends and comparisons by allowing for a global view of the data. It also allows members of the audience who may be less versed in numerical analysis to follow the information and understand the presentation more fully.

Displays multiple classes of data in one chart. Puts large sums of data into visual form for easy understanding. More visually appealing than other graphs….Disadvantages:

• Not visually appealing.
• Can be difficult to read with large amounts of data.
• Only works well with small sets of information.

What Are the Disadvantages of A Line Graph?

• Plotting too many lines over the graph makes it cluttered and confusing to read.
• A wide range of data is challenging to plot over a line graph.
• They are only ideal for representing data made of total figures such as values of total rainfall in a month.

The following are advantages of bar graph:

• Display relative numbers/proportions of multiple categories.
• Summarize a large amount of data in a visual, easily intepretable form.
• Make trends easier to highlight than tables do.
• Estimates can be made quickly and accurately.

Limitations of graphs

• No more than twelve attributes can be displayed on a graph.
• No more than two measurement types can be displayed on a graph.
• For example, if two statistics are measured in percentage and two in units, then all four appear in the graph because Y1 or Y2 allows a graph to have two like-measurements each.

Disadvantages of Bar Charts Only when bar charts show frequency distribution, each data category can be observed properly. Bar charts are very common and have lost impact on the readers. Bar charts often fail to mark key assumptions, patterns, and causes.

The major disadvantage of using charts and graphs is that these aids may oversimplify data, which can provide a misleading view of the data. Attempting to correct this can make charts overly complex, which can make their value in aiding a presentation less useful.

There are situations where “limitations” on graphs are needed to present realistic data. These limitations are referred to as “constraints”. Constraints are restrictions (limitations, boundaries) that need to be placed upon variables used in equations that model real-world situations.

If the y value being approached from the left is the same as the y-value being approached from the right (did the pencils meet?), that y value is the limit. Because the process of graphing a function can be long and complicated, you shouldn’t use the graphing approach unless you’ve been given the graph.

In order to say the limit exists, the function has to approach the same value regardless of which direction x comes from (We have referred to this as direction independence). Since that isn’t true for this function as x approaches 0, the limit does not exist.

If there is a hole in the graph at the value that x is approaching, with no other point for a different value of the function, then the limit does still exist.

To prove a limit does not exist, you need to prove the opposite proposition, i.e. We write limx→2f(x)=a if for any ϵ>0, there exists δ, possibly depending on ϵ, such that |f(x)−a|<ϵ for all x such that |x−2|<δ.

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( ) or less than or equal to ( ). The point is part of the solution. An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction.

When graphing a linear inequality on a number line, use an open circle for “less than” or “greater than”, and a closed circle for “less than or equal to” or “greater than or equal to”.

x. ′′​ The two sides of the equation have the same mathematical meaning and are equal. The open circle symbol ∘ is called the composition operator. We use this operator mainly when we wish to emphasize the relationship between the functions themselves without referring to any particular input value.

An open circle (also called a removable discontinuity) represents a hole in a function, which is one specific value of x that does not have a value of f(x). So, if a function approaches the same value from both the positive and the negative side and there is a hole in the function at that value, the limit still exists.

Limits allow us to study a number from afar. That is, we can study the points around it so we can better understand the given value we want to know. Especially in derivatives, where change in position is purely relative, the points around a given value are critically important.

The limit exists because the same y-value is approached from both sides. The closed circle is the actual y-value for when x=7.

The limit of a function doesn’t exist at a jump discontinuity, since the left- and right-hand limits are unequal.