Graph the equation. Describe the domain and range. 15. $$ y=\frac{1}{x} $$

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1. **Given Equation:**  
   $$
   y = \frac{1}{x}
   $$

2. **Graph Description:**  
   - The graph of $$ y=\frac{1}{x} $$ is a hyperbola.  
   - There is a vertical asymptote at $$ x = 0 $$ (the graph is not defined at $$ x=0 $$).  
   - There is a horizontal asymptote at $$ y = 0 $$ as $$ x $$ approaches positive or negative infinity.  
   - The hyperbola has two branches: one in the first quadrant (where both $$ x $$ and $$ y $$ are positive) and one in the third quadrant (where both $$ x $$ and $$ y $$ are negative).

3. **Domain:**  
   - The domain consists of all real numbers except where the function is undefined.  
   - Since division by zero is undefined, $$ x=0 $$ is excluded.  
   $$
   \text{Domain: } \{ x \in \mathbb{R} \mid x \neq 0 \}
   $$

4. **Range:**  
   - The range is all the possible $$ y $$-values that the function can take.  
   - As there is no $$ y $$ corresponding to $$ x=0 $$, and the output never equals 0, $$ y $$ can be any real number except 0.  
   $$
   \text{Range: } \{ y \in \mathbb{R} \mid y \neq 0 \}
   $$
The graph of $$ y = \frac{1}{x} $$ is a hyperbola with a vertical asymptote at $$ x = 0 $$ and a horizontal asymptote at $$ y = 0 $$. The domain is all real numbers except $$ x = 0 $$, and the range is all real numbers except $$ y = 0 $$.

Graph the equation. Describe the domain and range.
15.

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