Transformation involves changing the position of a function.
The new function is [tex]\mathbf{f"(x) = -|x| - 12}[/tex]
The function is given as:
[tex]\mathbf{f(x) = |x|}[/tex]
When the function is shifted 12 units up,
The rule of transformation is:
[tex]\mathbf{(x,y) \to (x,y+12)}[/tex]
So, the function becomes
[tex]\mathbf{f'(x) = |x| + 12}[/tex]
When the function is reflected in the x-axis,
The rule of transformation is:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
So, the function becomes
[tex]\mathbf{f"(x) = -(|x| + 12)}[/tex]
Expand
[tex]\mathbf{f"(x) = -|x| - 12}[/tex]
Hence, the new function is:
[tex]\mathbf{f"(x) = -|x| - 12}[/tex]
See attachment for the graphs of [tex]\mathbf{f(x) = |x|}[/tex] and [tex]\mathbf{f"(x) = -|x| - 12}[/tex]
Read more about transformations at:
https://brainly.com/question/13801312
