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Graphing And Functions

As we know that in a function each input value is instantly lined with one corresponding output value of that function. General concept of a graph is characterized by graph of relation. A function is always recognized by its graph but they are not same because it happens that two Functions that have different co- domain must have same graph. If we test graph of a function then we use vertical line test and if we test whether function is one – to – one then we use horizontal line test. If we have Inverse Function then graph of inverse function can be obtained by plotting graph of function along the line v = u. (here 'u' is along x - axis and 'v' is along y – axis. In a graph a curve is one – to – one function if and only if it is a function. Now we will try to understand Graphing and functions with help of an example.

Suppose we have a function: y = x – x2, we can plot graph of this function as shown below.
We need to follow some steps for Graphing Functions:
Step 1: Our function here is y = x – x2.

Step 2: We assume different values of x – coordinate to find values of y – coordinate.
If we value of x – coordinate as '0' then we get the value of y – coordinate as '0'. In same way if we put value of x – coordinate as -2, -1, 1, 2, 3 then we get value of y – coordinate as -6, -2, 0, -2, -6 respectively.

X

-2

-1

0

1

2

3

Y

-6

-2

0

0

-2

-6

 
 
Step 3: Now plot these coordinate on graph. So graph of given function is:
 
  
This is all about Graphing and Functions.

Topics Covered in Graphing And Functions

Graphing Lines

An equation is said to represent a line if highest power of variable it consists is 1. Most general form of linear equation representing a line is given as: y = mx + c Remember to resolve the equation if it is present in different form. Graphing Lines is an easy task to be done by working following steps:
 
In above equation “ c ” represents y- intercept. So, to start G...Read More

Graphing Circles

Circle is a conic section with its both axes (major and minor) equal in length. The key features of a Circle are its radius (half of the measure of any axis or Diameter), its circumference, chords (diameter being the longest), center, arcs, sectors etc. In other words a circle can be defined as Set of all those points which are equidistant from center Point. Circles can...Read More

definition of a function

The Definition of a Function in mathematics can be given as representation of relationship between a Set of variables and constants. These are used to solve equations for unknown variables. A function possesses unique output or value for each and every input given to it. A function in its simplest form can be written as: y = x. For any value of 'x' we insert in ...Read More

Combining Functions

In Algebraic calculations, you would most deal with the systems of Linear Equations that can also be correlated with finding the Combination of two Functions. Combining functions can Mean several possible operations like adding up two functions together, subtracting one function from the other, multiplying one function by the other, dividing one function by the other...Read More

Graphing Functions

In a function each input value is directly lined with one corresponding output value of that function. For example: If we have a relation that is defined by function rule f (s) = s2, then it compares its input’s’ to its Square, both values are real. If we put input value as -8 then we get its output as 64. In function form we can also write it as: f (-8) = 64. Real nu...Read More

Common Graphs

Graphs can be defined as plot of any expression or we can say representation of an expression on a graph. Here we will see some Common Graphs. Some common graphs are line graph, Parabola graph, Absolute value graph, Cubic gra...Read More

Graphing

Graphing can be defined as process of plotting Functions on graphs. Abstract equations, functions, expressions and concepts become more clearly visible when projected on an x - y coordinate plane, also known as a Cartesian coordinate system. This method for determining 'x' and y- coordinates for an equation becomes more complicated, going into the depth of mathematics.
 
The ...Read More

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