The modulus of a number is the magnitude of the number, that is it will give the value of the number disregarding the sign of the number, whether it is positive or negative.

The modulus is also called as absolute value of the number.

For ex: |7|=7 and |-7| =7

The modulus function returns the positive value of the expression.

|x| ={x ,x>0

{-x ,x<0

So we can see that whatever value the function takes ,the modulus will return the positive value.

We can take an example and explain this,

Let x takes the values 4,-5

So as we gives the values for x,in the definition:

|4| =4 (because 4>0)

now,assume x is taking the other value:

|-5|= -(-5) by definition

so it is 5(negative of a negative number is positive)

So in both cases the function returned the positive values.

Hence the definition.

F(x)=|x| is the basic modulus function

Let us take some values of x,both positive and negative, and we will find out the image

X= -5; |x| =5 so (-5,5) is a point

X= -4;|x| =4 so (-4,4) is a point

X= -3 ;|x| =3 so (-3,3) is a point

X= -2;|x|=2 so (-2,2) is a point

X=-1;|x|=1 so (-1,1) is a point

X=0;|x| =0 so (0,0) is a point

X=1 ;|x| =1 so (1,1) is a point

X=2 ;|x|=2 (2,2) is a point

X=3; |x|=3 so (3,3) is a point

X=4;|x|=4 so (4,4) is a point

X=5;|x| =5 so (5,5) is a point

Stuck on any of these topics **How to Graph Rational Functions**,
**the fundamental theorem of calculus** then keep reading my blogs i try to
help you.

Now let us graph the function:

We can see from the graph

1.The graph is fully above the x-axis

2.At (0,0) the graph turns

3.The graph is a join of two straight lines

4.As the value of x increases, y is also increases (increasing function)

5.The graph divides the first quadrant and the 3^{rd} quadrant in to 2 equal parts

6.The two lines of the graph intersect at origin ,and the lines are **perpendicular**