Continuous Graph

The continuous graph is the classic version of what we call a "graph", and it is a very important topic that reappears in almost all mathematics subjects.

What is a continuous graph?

A continuous graph is a linear graph that describes the continuity of numbers along the X horizontal axis.

A1 - What is a continuous graph

Each point on the continuous graph can be represented by an ordered pair (X,Y) (X, Y) where the left value in parentheses X X represents the numerical value of the horizontal axis, while the right value in parentheses Y Y represents the numerical value of the vertical axis.

Below is an example of a continuous graph

1- example of a continuous graph
  • In this graph, the X X axis represents time, while the Y Y axis represents speed.
  • The X X axis represents a continuous value of time and we observe in the graph how the speed changes as a function of time.

Sometimes graphs seem complicated, but if we understand how they work, we will see that they are actually very simple. A graph is just a way to show a lot of information at once.


We have several basic types of graphs. In this article, we will learn about discrete graphs

Another and different example

Example 1

A1 - Illustration 1 amount of water in the pool

Every graph is composed of two axes: the X X axis and the Y Y axis. The X X axis is the horizontal one (we can imagine it as the floor of the graph). In this graph, the X X axis will indicate the time. That is, as we move along the X X axis, the time will advance.

For example, you will be able to identify where the 12:00 12:00 hour is, then (to its right), the 13:00 13:00 and so on.

The Y Y axis is the vertical one (we can imagine it as the wall of the graph). In this case, it represents the amount of water in liters that is in the pool at each moment.

With the two axes, this graph describes the amount of water that is in the pool as the hours go by. That is, the pool is being filled with water over time, and the graph shows the amount of water at each given moment.


Sometimes graphs seem complicated, but if we understand how they work, we will see that, in reality, they are very simple. A graph is just a way to show a lot of information at once.

We have several basic types of graphs. In this article, we will get to know the continuous graph, learn how to read it, and how to draw it.


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Example 1: (We will continue with the last example)

A1 - Illustration 1 amount of water in the pool

Every graph is composed of two axes: the X X axis and the Y Y axis. The X X axis is the horizontal one (we can imagine it as the floor of the graph). In this graph, the X X axis will indicate the time. That is, as we move along the X X axis, the time will advance. For example, you can identify where the 12:00 12:00 mark is, then (to its right), the 13:00 13:00 mark, and so on.

The Y Y axis is the vertical one (we can imagine it as the wall of the graph). In this case, it represents the amount of water in liters that is in the pool at each moment.

With the two axes, this graph describes the amount of water in the pool as the hours pass. That is, the pool is being filled with water over time, and the graph shows the amount of water at each given moment.

Try to deduce:

  1. How many liters were in the pool at 12:00 12:00 ?
  2. When were there exactly 300 300 liters in the pool?
  3. How much water was in the pool at 14:30 14:30 ?

Let's answer the questions:

A2 - Illustration 2 amount of water in the pool

1.To understand how much water was in the pool at 12:00 12:00 sharp, we will look on the X X axis where the 12:00 12:00 mark is, then, we will see where the graph is on the X X axis at that time. In this case, we can see that, at 12:00 12:00 there were 0 0 liters of water in the pool. That is, at that time they began to fill it.

Illustration 2 amount of water in the pool

2.To find out when there were exactly 300 300 liters in the pool we will look on the Y Y axis for the mark that indicates 300 liters. We can even place our finger on that point on the Y Y axis. Then we will start moving to the right along the X X axis (moving our finger) until we meet the graph. We will realize that the meeting point with the graph is exactly above the 15:00 15:00 mark (indicated in the following graph). That is, at 15:00 15:00 sharp there were 300 300 liters of water in the pool exactly.

A3 - Illustration 3 amount of water in the pool

3.The question asked was how much water was in the pool at 14:30 14:30 ? The time 14:30 14:30 does not appear on the graph, but we know that it is exactly in the middle between 14:00 14:00 and 15:00 15:00 . Clearly, we can deduce where the 14:30 14:30 mark would be seen on the X X axis.

A4 - Illustration 4 amount of water in the pool

Now we can find out how much water was in the pool at that time: let's see where the graph is in relation to the Y Y axis exactly at the time 14:30 14:30 .

A5 - Illustration 5 amount of water in the pool

That is, at 14:30 14:30 there were exactly 200 200 liters of water in the pool.


What does continuous graph mean

In the previous article, we discussed the topic of discrete graphs. In the recent example and in those that follow, we see cases of continuous graphs. What do we mean when we write about a continuous graph?

A continuous graph is a linear graph that describes numerical continuity on the horizontal axis X X . For example, water filling a pool (the example just seen). The meaning of the word "continuous" is that it has no interruptions, that is, there is a continuity of data. Therefore, we will be able to deduce exactly how much water is in the pool at any given time.


Example 2 - Another example of a continuous graph

A car leaves at 7:00 7:00 from Madrid to Barcelona. Upon arrival, it stops. The graph describes the distance traveled by the car from its starting point.

A1 - The graph describes the distance traveled by the car from its starting point
  1. How far is the car from Madrid at 10:00 10:00 ?
  2. How far is the car from Madrid at 11:30 11:30 ?
  3. What time did the car reach its destination?

Solution:

1.To find out the distance between the car and Madrid at 10:00 10:00 we must find the hour 10:00 10:00 on the X X axis, then we will see where the graph of the function is in relation to that hour on the Y Y axis. In this case, the car is exactly 30km 30 km away from Madrid

A2 - Displacement of the car from Madrid to Barcelona

2.The hour 11:30 11:30 is not shown on the graph, but we know it is exactly in the middle between 11:00 11:00 and 12:00 12:00 . We can locate the precise place and find out where the graph is drawn, right at this point, in relation to the Y Y axis. We deduce that the car is exactly 50km 50 km away from Madrid. This deduction is possible because the graph is continuous.

A3 - Displacement of the car from Madrid to Barcelona

3.What time did the car reach its destination? The arrival time is not explicitly written, however, it has been explained that the car stopped upon arrival. That is, from a certain hour the distance between the car and Madrid should be fixed.

By observing the graph, we will see that, from 12:00 12:00 the car remains at a constant distance from Madrid, 60km 60 km . That is, that is the hour at which the car arrived at its destination and stopped. It can be seen that also at 13:00 13:00 and at 12:00 12:00 the car is still 60km 60 km away from Madrid.


If you are interested in more information about "graphs" you can find detailed information in the following articles:

Data Collection and Organization - Statistical Research

Reading Information from Graphs

Graph

Discrete Graph

Graphical Representation of a Function

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