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 – x^{2}.

**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 |

This is all about Graphing and Functions.

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