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

Answer 2

Linear functions can never be symmetric about the x-axis because;

It means it violates the vertical line test since we will have more than one output value for each corresponding input value as it is mirrored around the horizontal line.

In order to answer this question, we need to first understand the vertical line test.

• The vertical line test is a test that used to determine if a graph represents a function or not. This states that when any vertical line that intersects a graph curve more than once, then it means that such a graph does not define a function. This is because for it to be a real function, it must possess only one output value for each corresponding input value.

• Applying this to our question, linear functions can never be symmetrical about the x-axis because it means we will have more than one output value for each corresponding input value since it is mirrored around the horizontal line.

Read more at; https://brainly.com/question/1821791