Symmetry of Relations Within the Absolute Value
Could you please explain if/how the function f(x) = |2x+3| does not display even symmetry? I thought that any negative value within the absolute function becomes positive, making f(x)=(f-x) in that circumstance, however the math textbook I am using states that the equation is neither odd nor even.
Thank you for your question. The function f(x) = |2x+3| is neither odd nor even because it is not symmetrical with respect to the y-axis and it has no point symmetry. f(-x)=|2(-x) +3| = |-2x+3|. You can't just turn the negative to a positive in this case because there is also +3 there. Enter this function into Desmos to see what it looks like.