Can somebody explain the difference between monotone and continuous

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Monotonicity refers to the behavior of a function in terms of its increasing or decreasing nature as you move from left to right on a graph. A function is monotonic if it consistently increases or decreases without any interruptions. In contrast, continuity pertains to whether a function has any breaks, jumps, or holes in its graph. While a continuous function can be monotonic, not all continuous functions are monotonic, as they may increase and decrease at different intervals. Understanding these distinctions is crucial for grasping concepts in precalculus, especially as they relate to limits and graph behavior.
Imparcticle
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I don't entirely understand what is meant by monotonicity.

This is my situation: I am in precalc, (never taken it before), and we just did a lesson on on "conintuity, end behavior and monotonicity".
I was absent on this day, and I've been reading the lesson on my own. I understand continuity fairly well, I'm on the borderline between understanding and not for end behavior and I do not understand monotonicity. Now what don't I understand about monotonicity? I see that its just a method of understanding which way a graph increases from left to right, but then I end up getting it confused with continuity. That is, I don't see the difference between the two.
So, someone please explain everything they know about continuity and all others listed above simply. We have not gotten to limits yet, however, my teacher has it slightly incorperated into the lesson.

thanks
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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