Thread: Vertical / Horizontal Line Test

Hello!

I remember something from my pre-calc class about using a vert. and horiz. line test to determine something about a given graph.

If i'm not mistaken it was to determine if a graph is even or odd.

So, for example, if you take your pencil and slide the pencil across the graph keeping the pencil (or line) vertical at all times and you never touch more than one point on the graph with that pencil, then the graph is even and *may* have y-axis symmetry?

I feel like this is right. But then I was thinking. What about a graph that was just a big X centered on the origin that had both y and x-axis symmetry. This line test would not work since it would constantly be intersecting at two points.

Is it because an X on a graph like this is not a true function? Why is an X on the graph not a true function?

So, for example, if you take your pencil and slide the pencil across the graph keeping the pencil (or line) vertical at all times and you never touch more than one point on the graph with that pencil, then the graph is even and *may* have y-axis symmetry?

No, that means it's a function (that is, it's not multi-valued), as you are hinting at at the end of your post. The function is even if you can fold the function along the y axis, and the LHS will line up with the RHS. The function is odd if you can rotate the entire function graph 180 degrees, and it will leave the graph unchanged.

Incidentally, the horizontal line test (the same pencil-thing you mentioned) will tell you if the function is one-to-one.