Absolute value graphs are nothing but graph of the absolute values of numbers and functions. We know absolute value of any number is if it is positive or negative the absolute value
will be positive. So the absolute value of any number or functions graph will lies on the positive side. Here we are going to learn absolute value graph of the numbers and the absolute value
graph of the functions.

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Example problems of absolute value graphs for numbers:

**Example 1:**

Graph the absolute value of the number -9.

**Solution:**

Given number is -9.

Absolute value of |-9| is +9.

So the graph of the number -9 will be like the following

**Example 2:**

Graph the absolute value of the numbers -8, +5 and 3.

**Solution:**

Given numbers are -8, +5 and 3.

Absolute value of |-8| is +8

Absolute value of |5| is +5

Absolute value of |3| is +3

So the graph of the numbers will be like the following

These are the examples for absolute value graphs for numbers. Now we will see absolute value graphs for functions.

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Example for absolute value graphs for functions:

Graph the following **functions**: y = |x – 1| + 1

**Solution:**

To graph the function we have to give the value for x. here we are going to take the values -2, -1, 0, 1, 2 for
x.

x = -2 y = |-2 – 1| + 1= |-3| + 1 = + 4

x = -1 y = |-1 – 1|+ 1= |-2| + 1 = + 3

x = 0 y = |0 – 1|+ 1= |-1| + 1 = + 2

x = +1 y = |1 – 1|+ 1= |-0| + 1 = + 1

x = 2 y = |2 – 1|+ 1= |1| + 1 = + 2

Likewise we have to give the value. If we mark these points on the graph we will get the graph like this. When we graph this
function the graph will be shifted 1 unit upwards and 1 unit left.

These are the examples for absolute value graphs for functions.