Answer
Vertical stretch by a factor of $4$, shift $1$ unit upwards.
Work Step by Step
The graph of
$$
y=\frac{4}{x}+1
$$ is similar to the graph of the parent equation, $y=\frac{1}{x}$, which is a curve that passes through Quadrants I and III. The graph of the given equation, though, is vertically stretched by a factor of $4$ which causes the curve to have a narrower opening, followed by a shift $1$ unit upwards.
