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.
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.
More math articles
- Is a Calculator Allowed on the CBEST Test?
- 8th Grade STAAR Math FREE Sample Practice Questions
- How to Graph Quadratic Functions?
- Best Back-to-School Math Apps for Students
- How To Get A Perfect Score Of 800 On SAT Math?
- Number Properties Puzzle – Challenge 21
- Number Properties Puzzle – Challenge 4
- 4th Grade MAP Math Worksheets: FREE & Printable
- How to Write Linear Equations? (+FREE Worksheet!)
- Top 10 Praxis Core Math Prep Books (Our 2022 Favorite Picks)