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Math Help - Increasing & Decreasing Functions

  1. #1
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    Increasing & Decreasing Functions

    What is the difference between an increasing and decreasing function?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    What is the difference between an increasing and decreasing function?
    1. A function f(x) on the real line is increasing if:
    for all x, y in R, such that if x>y, then f(x)>=f(y).

    2. A function f(x) on the real line is strictly increasing if:
    for all x, y in R, such that if x>y, then f(x)>f(y).

    3. A function f(x) on the real line is decreasing if:
    for all x, y in R, such that if x>y, then f(x)<=f(y).

    3. A function f(x) on the real line is strictly decreasing if:
    for all x, y in R, such that if x>y, then f(x)<f(y).

    1a. A function f(x) on an interval I of the real line is increasing if:
    for all x, y in I, such that if x>y, then f(x)>=f(y).

    2a. A function f(x) on an interval I of the real line is strictly increasing if:
    for all x, y in I, such that if x>y, then f(x)>f(y).

    3a. A function f(x) on an interval I of the real line is decreasing if:
    for all x, y in I, such that if x>y, then f(x)<=f(y).

    3a. A function f(x) on an interval of the real line is strictly decreasing if:
    for all x, y in I, such that if x>y, then f(x)<f(y).



    RonL
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  3. #3
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    R

    I understood your words.

    However, what does the upper case R mean?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    I understood your words.

    However, what does the upper case R mean?
    It is the set of all real numbers. Often written \mathbb{R}.

    RonL
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