Question

What is the difference between discontinuities and zeros?

Answer 1

i believe discontinuities are holes in the graph...the part of the graph where the equation does not exist

zeros are the intersections of the graph with the axes

Answer 2

being discontinuous means a functions limit is not equal to the function itself/holes.
While zeros would mean roots. When you see zeros, we apply the intermediate value theorem.

Answer 3

that empty circle is the discontinuity...the zeros would be the intersection with the x and y axes

Answer 4

I see. Great! Thank You Both!!!

Answer 5

For example, a question may ask, show that cosx-1 has zeros in the interval [0,1]
or they may ask show that cosx-1 has roots in the interval [0,1], so we use intermediate value theorem to prove this