What the app does
If 0 belongs to the domain, f(0) gives the point on the y-axis. For the x-axis, f is sampled densely and every sign change is narrowed down by bisection, which also catches roots where the curve touches the axis without crossing it.
Why it matters
These are the points you can plot exactly, with no estimation. The roots also divide the domain into the intervals used in the next step, since a continuous function cannot change sign without passing through zero.
Read further
- Zero of a function Wikipedia
- y-Intercept Wolfram MathWorld
- Root Wolfram MathWorld