Consider the following function:
My book says this is its contour plot:
I don't understand why. I would have expected the lines to get closer together as you get closer to the X-Axis, yet they get further apart. I mean the the parabola converges to a single line at the x-axis, so shouldn't the lines be getting closer as you get closer to the X-axis?
Could someone explain why I'm wrong or help me see why the contour plot is correct?
Maybe thinking about the increase in steepness in the positive and negative $y$ direction will help (darker lines being steeper).
Alternatively you can somewhat see that the graph is $z=y^2$ so at each $z=c$ you have the two lines $y=\pm\sqrt{c}$. For example, for $z=9$, the two lines are $y=3, y=-3$. You can see that the lines get farther away from the origin but they remain straight lines.