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Answer:
f(x)= 3*(-|x+4|+5)
Step-by-step explanation:
Given the function f(x)=|x|
1. Transform the graph in a reflection across the x-axis:
You can transform the graph multiplying it by -1, so you have:
f(x)= -|x|
2. Translate the graph 4 units to the left:
You can translate the graph adding the number inside the absolute value, so:
f(x)= -|x+4|
3. Translate the graph up 5 units:
You can translate the graph up adding the number of units, but outside the absolute value, then:
f(x) = -|x+4|+5
4. Finally to transform the graph with a vertical stretch with a scale factor 3:
You should multiply the function by 3
f(x)= 3*(-|x+4|+5)
