If the graph of $y=f(x)$ is symmetric about the line $x=0$ (indicating an even function), what is the equation of the line of symmetry for the transformed graph $y=f(x-5)$?

A quadratic function is defined as $f(x)=(x-2{)}^2+5$. A horizontal translation is applied to create the function $$g(x)=(x+3{)}^2+5$$ Describe the translation that occurred.

Consider the graphs of $y=f(x-2)$ and $y=f(x+3)$. For any shared $y$-value in their range, what is the horizontal distance between the corresponding points on these two graphs?

Which of the following properties of the graph of $y=f(x)$ is invariant (remains unchanged) under a horizontal translation of $h$ units?

The graph of $y=f(x)$ undergoes two consecutive transformations: first, it is translated 4 units to the right, and then the resulting graph is translated 6 units to the left. What is the equation of the final transformed graph?