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.
Transformations
The given equation is a transformation of the parent functionf(x)=∣x∣. We can define each transformation from the inside to the outside. We will start with the transformation closest to x and end with the farthest from x. Let's review our function.
v(x)=-3∣x+1∣+4
First, there is a horizontal translation1 units to the left, ∣x∣⇒∣x+1∣. Remember, typically ∣x−h∣ is a horizontal translation h units to the right, while ∣x+h∣ is translated h units to the left.
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