Page 172 - DMTH201_Basic Mathematics-1

Unit 6: Functions

6.1.3 Classification of Functions Notes

Depending upon the nature of their symbolic expressions, various functions can be classified
into the into different categories. A brief description of some common types of functions is
given in the following sections.

Polynomial Functions

A function of the form y = a + a x + a x + ..... + a x , where n is a positive integer and ab a 0 ,
n
2
0 1 2 n n
is called a polynomial function of degree n.
(i) If n = 0, we have y = a , a constant function.
0
(ii) If n = 1, we have y = a + a x, a linear function.1
0 1
2
(iii) If n = 2, we have y = a + a x + a x , a quadratic or parabolic function.
0 1 2
3 3
2
(iv) If n = 3, we have y = a + a x + a x + a x , a cubic function etc.
0 1 2
Constant Functions
A function of the form y = f(x) = a for all real values of x, is a constant function. Graph of such a
0
function is a horizontal straight line with equation y = a , as shown in Figure 6.10.
0
Figure 6.10

0

0

0

Linear Functions

y = a + a x(a 0) is a linear function. The graph of the linear function is a straight line. Here a
0 1 1 0
is the value of y when x = 0, known as the intercept of the line on y-axis and a is the slope of the
1
line. If a > 0, the line slopes upward and when a < 0, the line slopes downward, as shown in
1 1
Figure 6.11 (a) and 6.11 (b) respectively.

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