e. \( y=\frac{1}{x}+3 \)

1. **Identify the parent function:** The function \( y=\frac{1}{x}+3 \) is based on the parent function \[ y=\frac{1}{x}. \] 2. **Determine the transformation:** The function has an added constant \( +3 \). In functions, adding a constant outside the function translates the graph vertically. Here, \( +3 \) shifts the graph upward by 3 units. 3. **Conclusion on the transformation:** \[ y=\frac{1}{x}+3 \] is the graph of \( y=\frac{1}{x} \) shifted upward by 3 units. - The **vertical asymptote** remains unchanged at \( x=0 \) (because adding a constant does not affect vertical asymptotes). - The **horizontal asymptote** of \( y=\frac{1}{x} \) is \( y=0 \). After shifting upward by 3 units, the horizontal asymptote becomes \[ y=3. \]