Graph the function and apply the appropriate transformations $y = (1)/( x + 4)$

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Graph the function and apply the appropriate transformations $y = 1/( x + 4) $

I know this much. My denominator can not be zero, thus $x+4 \neq 0$ which gives me $x > -4 $; in interval notation, $(-\infty,-4)\cup(-4,\infty)$.

Now if I was to sketch the graph (not exactly) the end behavior would be:

  • as $x$ approaches $-\infty $, $y$ approaches $-\infty $
  • when x approaches $\infty,$ $y$ approaches $\infty $

Am I correct?

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The interval you got is correct, but not because $x + 4 > 0$ but because $x + 4 \neq 0$

The second part of the exercise is wrong: As $x$ approaches to $+\infty $ you get y = $\frac{1}{smth\ BIG}$ which tends to $0^+$

In the same way, as $x$ approaches to $-\infty $ you get y = $\frac{1}{smth\ (-1)BIG}$ which tends to $0^-$