The image you've provided contains the graph of a transformed trigonometric function, specifically the tangent function, and instructions for adjusting its vertical stretch, horizontal asymptotes, and overall placement.

The function represented in the graph is:

$f(x) = \frac{5}{2} \tan \left( x - \frac{5\pi}{4} \right) + 4$

Analysis of the Transformation:

1. Vertical Stretch: The factor $\frac{5}{2}$ in front of the tangent function causes a vertical stretch by a factor of $\frac{5}{2}$. This means that the amplitude of the graph (the distance from the midline to the peaks and troughs) is increased by this factor.

2. Horizontal Shift: The term $x - \frac{5\pi}{4}$ inside the tangent function indicates a horizontal shift to the right by $\frac{5\pi}{4}$ units.

3. Vertical Shift: The term $+ 4$ outside the tangent function shifts the entire graph upward by 4 units, moving the midline from $y = 0$ to $y = 4$.

4. Asymptotes: The tangent function has vertical asymptotes where the argument of the tangent function is an odd multiple of $\frac{\pi}{2}$. With the horizontal shift of $\frac{5\pi}{4}$, the asymptotes are adjusted accordingly.

Would you like further details on any of the transformations or any help with the graph itself?