Can somebody explain the difference between monotone and continuous

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SUMMARY

Monotonicity refers to the behavior of a function in terms of its increase or decrease across its domain. A function is monotonic if it is either entirely non-increasing or non-decreasing. In contrast, continuity ensures that a function does not have any breaks, jumps, or holes in its graph. Understanding these concepts is crucial for analyzing functions in precalculus, particularly when studying their end behavior. The distinction lies in the fact that monotonicity focuses on the direction of the function's values, while continuity concerns the function's overall smoothness.

PREREQUISITES
  • Understanding of basic function concepts
  • Familiarity with graphing functions
  • Knowledge of precalculus terminology
  • Basic comprehension of limits (to be learned later)
NEXT STEPS
  • Study the definition and properties of monotonic functions
  • Learn about continuous functions and their characteristics
  • Explore the concept of limits and their role in continuity
  • Practice graphing functions to visualize monotonicity and continuity
USEFUL FOR

Students in precalculus, educators teaching function analysis, and anyone seeking to clarify the concepts of monotonicity and continuity in mathematics.

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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