Answer:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]
Step-by-step explanation:
The function that was transformed is:
[tex]f(x)=\lvert x\rvert[/tex]
If it reflects in the x-axis, shift 7 units to the right, and shift upward 2 units, we need to know the transformation rules for these displacements:
[tex]\begin{gathered} \text{ -f(x) reflects the function in the x-axis (upside-down)} \\ f(x-b)\text{ shifts the function b units to the right.} \\ \text{ f(x)+b shifts the function b units upward.} \end{gathered}[/tex]
Now, with this in mind, the equation of the function transformed would be:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]
