Question 226510
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x|y|\ =\ x\ +\ 9]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |y|\ =\ \frac{x\ +\ 9}{x}]


Using the definition of absolute value:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ \left\{\ \ x\text{ if }x\ \geq\ 0\cr-x\text{ if }x\ <\ \,0\right]


We can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{x\ +\ 9}{x}\ \ ] <b><i>OR</i></b> *[tex \LARGE \ \ y\ =\ -\frac{x\ +\ 9}{x}\ \ ]


Let *[tex \Large x\ =\ 1], then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1\ +\ 9}{1}\ =\ 10]


<b><i>OR</i></b>


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{1\ +\ 9}{1}\ =\ -10]


Therefore, <b><i>NOT a function</i></b>



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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