GRAPHS ON THE GO : INTRODUCTION

When it comes to analyse quantities and reading curves , graphs play an essential role. So this series named "GRAPHS ON THE GO" is designed for those who struggle to read, draw and understand graphs. This series will start from basic and will boost you upto the maximum you need.

Graphs are drawn in a plane called cartisian plane which consists of Horizontal axis X and vertical axis Y extending infinitely both sides.
The cartisian plane looks like this-

All the points which exists in this plane are represented by (x,y) in general where x represents the distance moved along x axis and y represents the distance moved along y axis also the intersection of these axis is called origin(0,0).

If they have a sign along with them this implies that the sign signifies which direction on axis the point moved - represents along negative side and + represents the positive side.

Also it is right time to know the basic definition of a FUNCTION.
So we can consider function as a machine in which we give in some input and expect a specific result to come out.

The most important thing to note about a function is that it gives a unique value for any input, simplifying - it will yeild only one output for a particular input.

Now Let's move towards Graphs.

Before diving deep into this ocean of GRAPHS we need to learn some basic graphs.

1. STRAIGHT LINE:  A straight line has general form of y = mx + c, where m is the slope of the line and c is the intercept cut by it at y axis. Slope represents the tan of angle with which the line incline with positive x-axis. In the above graph the value of slope is 1 and intercept cut by it is 5. 

2. INDENTITY FUNCTION: The above graph is basically a straight line with slope 1 and y intercept 0 but it holds a special importance. This function plotted above is called indentity function because it composition any function and its inverse results out this function hence it also helps to plot the graph of inverse of a particular function(which we will see in later posts).

3. CONSTANT FUNCTION: This is also a straight line with slope 0 and y intercept 5. This is called constant as it results out the same output for every input in this function. Also through graph it is quite clear that for any value of x the value of y is constant( 5 in this case).

4. It also acts as a constant function but the difference is that it is along y axis and gives a constant value of x for any value of y.

5. PARABOLA

6. SQUARE ROOT

7. EXPONENTIAL FUNCTION: This curve holds its significance at many places where the growth is very fast like in business(if  it is growing at a fast pace, its profit graph is similar to this curve), in first order reaction the decayed nucleus can be represented using the same graph.

5. CUBIC FUNCTION

8. MODULUS FUNCTION: This is a type is which for every input it gives out the absolute value of that input or it makes every input and result its positive equivalent. As it is evident from the graph that for both +2 and -2 input we the the positive equivalent(=2) of it as output.

9. Greatest Integer Function: This results out the greatest integer which is equivalent or before the the number passed into this function. Example- 

for x = 2.3 , it will result out 2 

for x = -2.3 it will result out -3 

for x = 2 it will result out 2

for x = -2 it will result out -2.

It always the output as integer.

10. Fractional Part : This results out the fraction part of the input, It is also defined as

{x}  = x - [x]

Example-

for x = 2.3 it will result out 2.3 - 2 = 0.3

for x = -2.3 it will result out -2.3 - (-3) = 0.7

11. Signum function : This function is used in switching logics and it is defined as follows-

for x > 0 it will result out , 1.

for x < 0 it will result out , -1.

for x = 0 it will result out , 0.

Stay Tuned for the next post.

For any query comment down there.

#graphs_on_the_go  #understanding_graphs #mathematics, #feed-o-math , #quadratic_equations

(Image credits- https://www.desmos.com/)