Question

Why are linear functions sometimes symmetric about the y-axis but never symmetric about the x-axis

Answer 1

Test for symmetry about the x-axis: Replace y with (-y). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the x-axis. Example: Use the test for symmetry about the x-axis to determine if the graph of y - 5x2 = 4 is symmetric about the x-axis.
Test for symmetry about the y-axis: Replace x with (-x). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the y-axis. Example: Use the test for symmetry about the y-axis to determine if the graph of y - 5x2 = 4 is symmetric about the y-axis.
I didn't fully understand the question but this is the best I can do! Hope this helps! :D