Final answer:
Reflecting a function over the x-axis inverts it vertically, and reflecting over the y-axis results in a horizontal mirror image. The correct answer is (d) Mirrors the function across the x and y-axes. This is seen in the properties of even and odd functions regarding symmetry and reflection.
Step-by-step explanation:
Reflecting a function over an axis corresponds to mirroring the function across that axis. Reflecting over the x-axis changes the sign of the y-coordinates of points on a graph, resulting in a function that is upside down from the original. Reflecting over the y-axis changes the sign of the x-coordinates of points on a graph, creating a mirror image of the original function on the other side of the y-axis.
Therefore, the correct answer to what reflecting over each axis does to a function in Algebra 2 is (d) Mirrors the function across the x and y-axes. This transformation does not affect the domain of the function (which would be answer choice a), and it does not necessarily reverse the direction of the function or change the y-intercept unless the original function had a specific orientation or y-intercept that is affected by reflection (eliminating b and c as correct responses).
An example of reflection can be seen when looking at even and odd functions. An even function is symmetric about the y-axis, which means it looks the same on both sides of the y-axis. In contrast, an odd function (or anti-symmetric function) looks the same when it is reflected around the y-axis and then the x-axis.