CA/CPT 2011 Preparation, Online Commerce Study Material, CA/CPT Test Papers, Syllabus Books & Results

Manasi

Functions are usually expressed by formulae. But the techniques of graphical representation of function are of immense value in mathematics.. Moreover, various areas of mathematics are rendered easy if solved thru using there graphs... if u r knowing the graph of y = f(x).. Then here are few techniques to draw some graphs -

Case 1

To draw the graph of form y = a+ f(x) (graph 1)

Draw the graph of y = f(x) (in yellow) and then shift the graph 'a'unit above if a>0(in red), or shift it 'a' unit below if a < 0 (in red)

Case 2

To draw the graph of form y = f(x+a) (graph 2)

Draw the graph of y = f(x) and then shift the graph 'a' unit towards the right of y-axis if a>0 (in purple), or shift it 'a' unit towards left of y-axis if a < 0 (in red)

Case 3

To draw the graph of form y = af(x) (graph 3 )

This graph is similar to the shape of y= f(x)... but the size gets hanged, i.e. y gets changed while x is constant!

here shown with a particular example of y =a sin x ...with the help of graph of y = sin x.. where a has values 1 [graph of y = sin x(in yellow)], 2 [graph of y = 2 sin x(in red)], and 3 [ graph of y = 3sin x (in purple)],

scale :

x-axis : pi/2

y-axis : 1

PS: pls click on the figures to enlarge it...