# 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.

## A 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 GraphingAbsolute Value Function

### Graph followingabsolute 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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