Let f (x) = |x| for all real numbers x. Write the formula for the function represented by the described

transformation of the graph of y = f (x).

c. First, a reflection across the xx-axis is performed, then a translation left 4 units, then a translation up 5 units,

and finally a vertical stretch with scale factor 3

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)