Question

Let f(x)= |x|. Write a function g whose graph is a reflection in the the x axis followed by a translation 4 units to the left of the graph of f

Answer 1

Remember the general rule of transformation:

1) Horizontals Shifts:

y=f(x+h); Shifts the graph of f left h units if h>0, Shifts it right |h| units if h<0

2) y= - f(x), Reflects the graph of f across the x-axis.

In our question,

f(x)= |x|

Now,

g(x)= -|x+4| , (new function: reflected across x-axis and translated 4 units to the left )

The graph is attached below.