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Math Help - constant functions

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    constant functions

    Hello, I am currently studying a section in my math book entitled "Increasing and Decreasing Functions," but my inconvience dwells in my contention with what the author states about a constant function.

    Here is a picture of the figure they give me in the book

    2011-07-01_10-12-23_898.jpg picture by Bashyboy - Photobucket

    The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).

    So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule. I appreciate any whom try to answer.
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    Re: constant functions

    Quote Originally Posted by Bashyboy View Post
    The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).
    So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule.
    The rule simply states that in terms of ordered pairs, every pair has the same second term for any x in the interval.
    The graph is the set \{(x,c):x\in(a,b)\}.
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    Re: constant functions

    Quote Originally Posted by Bashyboy View Post
    Hello, I am currently studying a section in my math book entitled "Increasing and Decreasing Functions," but my inconvience dwells in my contention with what the author states about a constant function.

    Here is a picture of the figure they give me in the book

    2011-07-01_10-12-23_898.jpg picture by Bashyboy - Photobucket

    The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).

    So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule. I appreciate any whom try to answer.
    Hi Bashyboy,

    A constant function is f(x)=C, where C is a constant.

    Your function decreases until x = 0. f(0) = 1.

    Your function is constant on the interval [0, 2].

    For every x in the interval [0, 2], f(x) = 1.

    An application of the rule would be:

    \text{Given: }x_1=0 \text{ and } x_2=2 , f(0)=f(2)=1
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