Hey guys, I'm reading The Complete Idiot's Guide to Calculus and I think the book made a mistake.
Here is a picture of a graph that the author claims to have "origin-symmetry":
And here is his description of this graph. When the author mentions Figure 3.4, he is mentioning the graph he claims to have "origin-symmetry".
To me, it looks like it actually has y-symmetry!Origin-symmetry is achieved when the graph does exactly the opposite thing on either
side of the origin. In Figure 3.4, notice that the origin-symmetric curve snakes down and
to the right as x gets more positive, and up and to the left as x gets more negative. In fact,
every turn in the second quadrant is matched and inverted in the fourth quadrant.
If it had origin-symmetry, the graph to the right of the origin should be in quadrant 4, not quadrant 1! Because when x>0, y must be negative. And when x<0, y must be positive.
And when the author says "the origin-symmetric curve snakes down and to the right as x gets more positive", you can plainly see that the curve actually snakes up and to the right when x gets more positive
Is this book actually wrong on this subject?
Thanks for your time!