7. Graphing Absolute Value Functions
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To graph the functions without going through the entire process of transforming the parent function, we can make two tables of values. Then we only need to plot the ordered pairs that we find.
Let's begin with creating a table of values of function v.
x | -2∣3x+1∣+4 | Simplify | v(x) |
---|---|---|---|
-2 | -2∣3(-2)+1∣+4 | -2∣-5∣+4 | -6 |
-31 | -2∣∣∣∣∣3(-31)+1∣∣∣∣∣+4 | -2∣0∣+4 | 4 |
0 | -2∣3(0)+1∣+4 | -2∣1∣+4 | 2 |
1 | -2∣3(1)+1∣+4 | -2∣4∣+4 | -4 |
Now it is time for doing the same with function w.
x | 3∣3x+1∣−6 | Simplify | w(x) |
---|---|---|---|
-1 | 3∣3(-1)+1∣−6 | 3∣-2∣−6 | 0 |
-31 | 3∣∣∣∣∣3(-31)+1∣∣∣∣∣−6 | 3∣0∣−6 | -6 |
0 | 3∣3(0)+1∣−6 | 3∣1∣−6 | -3 |
1 | 3∣3(1)+1∣−6 | 3∣4∣−6 | 6 |
Finally we can take these ordered pairs and plot them on one coordinate plane.
As we can see from the graphs, the function w is a vertical stretch by a factor of 23 and a reflection in the x-axis of the graph of function v.