7. Graphing Absolute Value Functions
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First we will go through all the transformations from the graph of f(x)=∣x∣ to the graph of given function. After that we will make a table of values to graph this function.
Next, we have a vertical translation 4 units up, ∣x+4∣⇒∣x+4∣+4. Remember, in most cases ∣x∣+k is a vertical translation k units up, while ∣x∣−k is translated k units down.
To graph the function without going through the entire process of transforming the parent function, we could instead make a table of values. Then we only need to plot the ordered pairs that we find.
x | ∣x+4∣+4 | Simplify | c(x) |
---|---|---|---|
-8 | ∣-8+4∣+4 | ∣-4∣+4 | 8 |
-6 | ∣-6+4∣+4 | ∣-2∣+4 | 6 |
-4 | ∣-4+4∣+4 | ∣0∣+4 | 4 |
-2 | ∣-2+4∣+4 | ∣2∣+4 | 6 |
0 | ∣0+4∣+4 | ∣4∣+4 | 8 |
Now we can plot these points and connect them to create our graph of c(x).