Absolute value function
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Absolute value function is one of the topics in which we are going to see about solving for x in absolute value and graphing the absolute-value-function.

Absolute value: The absolute value of a number is its distance from 0 on a number line. For example, the number "9" is 9 units away from zero. So its absolute value is 9. Negative numbers are more interesting compared to positive numbers,because the number -4 is still 4 units away from 0. The absolute value of the number -4 is therefore positive 4 .

Examples of absolute value:

The absolute value of -9 is 9 The absolute value of 5 is 5 The absolute value of 0 is 0 The absolute value of -256 is 256 More examples of absolute value:

| -5 + 8 | = 3

| -8 x 2 | = | -16 | = 16

| -13 + 5 | = | -8 | = 8

Example problem of solving x in absolute values

| x + 9 | = 5 Solution:

x + 9 = 5 (or) x + 9 = -5

x = 5 – 9 (or) x = -5 -9 x = -4 (or) x =-14

The solution is -4 and -14 | x - 8 | = -9 Solution:

x – 8 = -9 (or) x - 8 = 9

x = -9 + 8 (or) x = 9 + 8 x = -1 (or) x = 17 The solution is -1 and 17

Graphing absolute value function
| x | > 2

Before graphing we need to write the given function as the following

x > 2 (or) x < -2

Therefore the interval notation is (-infinity,-2) and (2, + infinity)

| x | = 4 x = 4 or x =-4

More examples for graphing

An absolute value equation graphs like a "V".

General form for Absolute function y = a |x – h| + k or y – k =a|x-h|. Here (h, k) is vertex. If “a” is positive the graph will be open upward If “a” is negative the graph will be open downward. y = | x -1| Here we need to consider the given question as y-k = a |x-h| Comparing with general form now we haveY-0 = |x -1| So the vertex is (1, 0) and instead of a we have +1.so the graph will be open upward.To find the x-intercept we have to put y=0 so that we will get x =1.There fore the x-intercept is 1.
y = |x-1|-2

y + 2 = |x-1|

Here vertex is (1,-2) and the graph will be open upward because the value of a is positive.

x-intercept:

put y=0

x – 1 = 2 or x – 1 = -2

x = 2 + 1 or x = -2 + 1

x = 3 or x = -1

By using the above problems you can understand the topic absolute value function better.

Number line Algebra