Well, technically a tangent like can cross at multiple points. For example in the graph to the left the tangent line passes through the graph twice. A tangent line is not a line that crosses a function once. A better way of explaining it would be to imagine the tangent line crossing the curve at point P would be to define point Q as any other point on the curve. The secant line joining point P and point Q would become the tangent line when Q is brought to and is point P.
So a tangent line could possible cross a line an infinite number of times (An easy example would be either tangent line with slope = 0 on either the sin or the cos functions.)
Please teach me. I'm in college, and the math is insane. I will gladly pay you to tutor me D:
Just go easy on the price, I am unemployed, but if I
am spending a portion of my life savings on this, it should
be worth it in the long run