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:
Let us take some random values for \(x\).
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 \(y=|x−1|\).
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.
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