7. Graphing Absolute Value Functions
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Create two tables of values and then plot the graphs on the same coordinate plane.
Graph:
Comparison: See solution.
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 w.
x | ∣x−3∣+4 | Simplify | w(x) |
---|---|---|---|
-2 | ∣-2−3∣+4 | ∣-5∣+4 | 9 |
0 | ∣0−3∣+4 | ∣-3∣+4 | 7 |
2 | ∣2−3∣+4 | ∣-1∣+4 | 5 |
4 | ∣4−3∣+4 | ∣1∣+4 | 5 |
Now we will do the same with function y.
x | ∣5x−3∣+4 | Simplify | y(x) |
---|---|---|---|
-1 | ∣5(-1)−3∣+4 | ∣-8∣+4 | 12 |
53 | ∣∣∣∣∣5(53)−3∣∣∣∣∣+4 | ∣0∣+4 | 4 |
1 | ∣5(1)−3∣+4 | ∣2∣+4 | 6 |
2 | ∣5(2)−3∣+4 | ∣7∣+4 | 11 |
Finally we can plot these ordered pairs on one coordinate plane.
We can rewrite y(x) as w(5x), which is a horizontal shrink by a factor of 51. It is being shrunk closer the y-axis. Note that when the x-values of w are five times the x-values of y, the y-values stay the same.