Introduction to Graphing

A graph in mathematics is a visual representation that helps explain a concept by showing data or values in an ordered manner. The graph’s points show the relationship between two or more variables.
What are Types of Graphs?
Graphs can be of various types such as points, curves, polygons, circles, and straight lines, based on the types of data and purpose. 

Let us examine different kinds of graphs and charts.

• Pictograph
• Bar Graph
• Line Graph
• Pie Chart
• Pictograph

A pictograph, or picture graph, visually represents data using images, symbols, or icons to make numerical or categorical information easier to understand and more engaging.
For example, each symbol in the graph represents a specific number of apples sold by different vendors.

 Bar Graph

 A bar graph is a graphical display of numbers, quantities, or data that uses bars or strips. They are employed to compare and contrast various data types, frequencies, or other metrics of discrete data categories. For example,

The graph displays the number of students who prefer each season. The graph’s bottom horizontal axis displays the seasons: spring, summer, fall, and winter. The vertical axis displays the number of students as 0, 1, 2,...

Line Graph 

A line graph, sometimes referred to as a line chart or a line plot, is frequently created to display data that evolves over time. Plotting a graph involves marking multiple points and connecting them to show the trend or shape of the data. The “x-axis” and the “y-axis” are its two axes.

Pie Chart

A circle graph is another name for a pie chart. It illustrates how a whole is broken down into its component parts. The relative size of each category compared to the whole is displayed in the pie chart. To show how much of the total each category makes up, percentages are utilized.

Drawing the curve that the function takes on a coordinate plane is known as graphing the function. If a curve represents a function, each point on it must satisfy the function’s equation. For example, the linear function’s corresponding graph is displayed below. The formula for it is f(x)=-x+2 

To check if a point lies on the line f(x)=-x+2, substitute its coordinates into the equation. For example, for (-1, 3):
3=-(-1)+23=1+23=3
Since the equation is true, the point satisfies the function. Other points can be tested in the same way to confirm they lie on the line. Creating curves for a function is called graphing the function.
 

Graphing is used in daily life, such as tracking resource consumption and monitoring weather changes. Let us see a few applications in graphing and how it helps in real life.

• Diabetic blood sugar monitoring
  Blood glucose levels are monitored throughout the day using line graphs. For example, a reading may rise from 90 mg/dL before breakfast to 150 mg/dL after eating, helping patients and physicians know trends, adjust treatment, and maintain safe glucose levels.
•  Monitoring students achievements
  Teachers compare students’ scores across terms or subjects using bar graphs. By highlighting a student’s strengths and areas for development, these visuals help support individualized learning approaches.
• Monitoring Covid-19 cases
  Health organizations display case trends on a daily or weekly basis using graphs. Authorities use rising or falling lines to inform their decisions about public health measures like easing restrictions or implementing lockdowns.
• Analysis of vehicle speed
  In driving tests or crash investigations, speed vs. time graphs show the vehicle’s speed at any given moment. Abrupt alterations in the graph may indicate collisions, braking, or acceleration. For example, if a vehicle accelerates uniformly from 0 m/s to 20 m/s in 5 seconds, the speed-time equation is,
• v=u+at
  Where, u = 0, v = 20, and t = 5, giving an acceleration a = 4 m/s2.
• Hospital heart rate monitoring
  The heart rate of a patient is tracked over time using graphs. Stability is indicated by a steady graph line that falls within the typical range. Doctors can identify deviations and treat patients promptly when they see abrupt spikes or drops on the graph.