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Graph each function; identify the domain and range; and compare the graph with the...

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anya4one | Student, Undergraduate | (Level 2) Honors

Posted July 20, 2013 at 3:54 PM via web

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Graph each function; identify the domain and range; and compare the graph with the graph of y=1/x.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 20, 2013 at 4:32 PM (Answer #1)

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You need to evaluate the domain of the function, hence, you should remember that the domain of the function needs to contain the values of x that validate the function.

The function `y = -10/x` contains `x` at denominator, hence, since division by 0 is undefined, you need to exclude the value 0 from the domain of definition.

Hence, evaluating the domain of definition of `y = -10/x` , yields `R - {0}` .

The range of the function is the set of real numbers `R` .

Comparing the graphs `y = 1/x` (black curves) and `y = -10/x` (red curves) yields that function `y = 1/x` first suffers a reflection through y axis, `y = -1/x` , and then a vertical expansion by the factor` k = 1/10` , becoming the final function `y = -10/x` .

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