How to "read" the following graph?

Question

The question is the following. How can I "see" from the following graph, that $f(-1) = f(1)$?

How can I recognize that, exactly?

Answer 1

Think of "$f(-1)=f(1)$" as saying "the height above $-1$ = the height above $1$".

Here, the "height" is the vertical distance above the given point on the horizontal number line, determined by the graph (possibly negative if the graph is below the horizontal number line at that point).

In your case, the graph is actually at height $0$ above $-1$ and at height $0$ above $1$, so they are the same.

You recognize this by seeing that the vertical segments which you mentally draw there are of the same height.

Likewise, you can see that $f(0)$ and $f(3.5)$ are roughly equal since the height of the graph is roughly $1$ at both of these points.