A function can be defined as a rule that relates how one quantity depends on other quantities. A function is a relationship between two variables. The first variable is called the independent variable (usually written as x), and the second variable is called the dependent variable (usually written as y). These variables are real numbers. In a function, each value for the independent variable corresponds to exactly one value for the dependent variable. Independent variable is also called as input and dependent variable is sometimes referred as output. A function can be represented as ordered pair, in tabular form, using graphical representation and with a mathematical expression. A function is written as f(x) and read as ‘function f of x’. We can use other letter also like y(x), g(x), P(x), h(x). A function can be solved for various values of independent variable.
The domain of a function is the set of all input values to which the rule of function applies. These are the values of independent variable. These correspond to the first (x) component of the ordered pairs representing the function.
The range is the set of output values. These are the values of dependent variable. These correspond to the second (y) component of the ordered pairs representing the function.
Example:
A = {(0, -1), (1, 0), (2, 1), (3, 2)}
Domain = {0, 1, 2, 3}
Range = {-1, 0, 1, 2}
Example:
|
Input |
Output |
|
-1 |
1 |
|
0 |
2 |
|
1 |
3 |
|
2 |
4 |
Domain = {-1, 0, 1, 2}
Range = {1, 2, 3, 4}
Example:
If f(x) = 2x – 3, what is f(-2), f(4) and f(5)?
While solving for these values x in the above expression gets replaced by values of x.
f(-2) = 2(-2) – 3 = -4 – 3 = -7
f(4) = 2(4) – 3 = 8 – 3 = 5
f(5) = 2(5) – 3 = 10 – 3 = 7
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