Consider the following table of the
function 𝑓 of 𝑥. We have 𝑥-values from one to four
and corresponding 𝑓 of 𝑥 values also from one to four. Choose the table of the reflected
function 𝑔 of 𝑥 over the 𝑦-axis.
We are given five options, (A) to
(E). After clearing some space, we will
plot the values in the table as points in the coordinate plane. The function 𝑓 of 𝑥 has four
coordinates in the table: the points one, one; two, two; three, three; and four,
four. We are told that the function 𝑔 of
𝑥 is the reflection of this in the 𝑦-axis. Reflecting each of the points of 𝑓
of 𝑥 in the 𝑦-axis gives us the coordinates negative one, one; negative two, two;
negative three, three; and negative four, four. The 𝑥-coordinates change sign and
the 𝑦-coordinates remain the same. 𝑔 of 𝑥 has 𝑥-values equal to
negative one, negative two, negative three, and negative four and corresponding
values of 𝑔 of 𝑥 or 𝑦 of one, two, three, and four. From the five options originally
listed, this was option (D).