# How to Graph Absolute Value Function?

The process of charting absolute value equations can be reduced to a few specific steps that help to develop any type of absolute value graph. In this step-by-step guide, you will become more familiar with the steps of graphing an absolute value function.

The absolute value represents the distance of a number on the number line from the origin, better known as zero. The absolute value of a number is never negative. It ignores in which direction from zero the number lies, it only matters how far it is.

**Related Topics**

**Step by Step guide to graphing absolute value function**

Let’s look at the most basic graph of the absolute value function, \(y=|x|\)

Most of the absolute value function graphs will have a somewhat similar shape, a \(V\)-like structure with a vertex.

The following steps will be useful in graphing absolute value functions:

**Step 1:**Before plotting any absolute value function, first, we must plot the absolute value parent function:

\(y=|x|\)

Let us take some random values for \(x\).

\(x=−3→y=|−3|=3→(−3,3)\)

\(x=−2→y=|−2|=2→(−2,2)\)

\(x=−1→y=|−1|=1→(−1,1)\)

\(x=0→y=|0|=0→(0,0)\)

\(x=1→y=|1|=1→(1,1)\)

\(x=2→y=|2|=2→(2,2)\)

\(x=3→y=|3|=3→(3,3)\)

If we plot these points on the graph sheet, we will get a graph as given below.

When we look at the above graph, clearly the vertex is \((0, 0)\).

**Step 2:**Write the given absolute value function as \(y−k=|x−h|\).**Step 3:**To get the vertex of the absolute value function above, equate \((x – h)\) and \((y – k)\) to zero, that is,

\(x−h=0\) and \(y−k=0\)

\(x=h\) and \(y=k\)

Therefore, the vertex is \((h, k)\).

**Step 4:**According to the vertex, we have to shift the above graph.

**Note:** If we have negative signs in front of absolute signs, we have to flip the curve over.

**Graphing Absolute Value Function** **– Example 1:**

Graphing absolute value function \(y=|x−1|\).

**Solution:**

The given absolute value function is in the form: \(y−k=|x−h|\)

That is, \(y=|x−1|\)

To get the vertex, equate \((x – 1)\) and \(y\) to zero.

\(x-1=0\) and \(y=0\)

\(x=1\) and \(y=0\)

Therefore, the vertex is \((1,0)\).

So, the absolute value graph of the given function is:

**Exercises for Graphing** **Absolute Value Function**

**Graph following** **absolute value function**.

- \(\color{blue}{y=\left|x+4\right|+4}\)

- \(\color{blue}{y=-\left|x-2\right|}\)

- \(\color{blue}{y=-\left|x\right|+3}\)

- \(\color{blue}{y=\left|x+4\right|+4}\)

- \(\color{blue}{y=-\left|x-2\right|}\)

- \(\color{blue}{y=-\left|x\right|+3}\)

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