1. The problem is to graph the function $y = \frac{1}{x} + 2$ by starting with the graph of the standard function $y = \frac{1}{x}$ and applying transformations. 2. The standard function is $y = \frac{1}{x}$, which is a hyperbola with vertical and horizontal asymptotes at $x=0$ and $y=0$ respectively. 3. The given function is $y = \frac{1}{x} + 2$. This means we take the graph of $y = \frac{1}{x}$ and shift it vertically upward by 2 units. 4. The vertical shift moves the horizontal asymptote from $y=0$ to $y=2$. 5. The vertical asymptote remains at $x=0$ because the denominator is still $x$. 6. So the transformed graph has vertical asymptote $x=0$ and horizontal asymptote $y=2$. 7. The shape of the hyperbola remains the same, just shifted up by 2. 8. To summarize, start with $y=\frac{1}{x}$, then apply the transformation $y \to y + 2$ to get $y=\frac{1}{x} + 2$. Final answer: The graph of $y=\frac{1}{x} + 2$ is the graph of $y=\frac{1}{x}$ shifted vertically upward by 2 units, with vertical asymptote $x=0$ and horizontal asymptote $y=2$.