MOD (| |) ------------ curves

HOW  DO  MODULUS EFFECT THE CURVES?? (y=f(|x|),y=|f(x)|….)

WHAT DOES MODULUS DO FIRST?

Simply it changes some quantity  positive or gives absolute value.

Here lets ‘x’ be some real number

|x|=    1. x , where x = positive real number.

             2. –x, where x = negative real number.  

  Now,

Lets us take a curve y=f(x),

Firstly you have to know how to draw the y=f(x) curve.

To draw the curve y=f(|x|),

draw

Y=f(|x|)        1. Y=f(x), for x=+ve values.

                      2.y=f(-x),for x=-ve values.

To draw the curve y=|f(x)|

Draw

Y=|f(x)|          1.y=f(x) , for f(x)=+ve values.

                         2. y=-f(x), for f(x)=-ve values.

Examples

Now  we will take the curve y=sin(x).

Sketch the graph of y=sin(x)

Now lets draw the curve y=-sin(x) and the graph of y=sin(-x) will be same because sin(-x)=-sin(x)

By now we are ready to draw the curves y=f(|x|),y=|f(x)|.

1.Y=f(|x|)  i.e y=sin(|x|)

    Draw 1.sin(x) for x = positive

               2.  sin(-x)=-sin(x) for x=negative     

2.y=|f(x)|  i.e y=|sin(x)|

Draw 1.sin(x) for sin(x)=positive (y=positive)

           2.-sin(x) for sin(x)=negative(y=negative)