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22 November, 08:55

What graph represents f (x) = x over the domain 3

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  1. 22 November, 09:22
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    Ex. 1) A piecewise function is usually defined by more than one formula: a fomula for each interval.

    Example 1:

    f (x) = - x if x < = 2

    = x if x > 2

    What the above says is that if x is smaller than or equal to 2, the formula for the function is f (x) = - x and if x is greater than 2, the formula is f (x) = x. It is also important to note that the domain of function f defined above is the set of all the real numbers since f is defined everywhere for all real numbers.

    Example 2:

    f (x) = 2 if x > - 3

    = - 5 if x < - 3

    The above function is constant and equal to 2 if x is greater than - 3. function f is also constant and equal to - 5 if x is less than - 3. It can be said that function f is piecewise constant. The domain of f given above is the set of all real numbers except - 3: if x = - 3 function f is undefined.

    Example 3:

    Functions involving absolute value are also a good example of piecewise functions.

    f (x) = | x |

    Using the definition of the absolute value, function f given above can be written

    f (x) = x if x > = 0

    = - x if x < 0

    The domain of the above function is the set of all real numbers.
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