Question Video: Using a Table of Values to Identify the Reflection of a Function in an Axis Mathematics

Consider the following table of the function 𝑓(𝑥). Choose the table of the reflected function 𝑔(𝑥) over the 𝑦-axis.

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Video Transcript

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).

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