Here is the sketch of the graph for the function $f(x) = \frac{4x - x^2}{x^2 - 5x + 4}$. Key features:

1. Vertical asymptotes at $x = 1$ and $x = 4$.
2. Horizontal asymptote at $y = -1$.
3. The function behaves as expected near these asymptotes, diverging to $\infty$ or $-\infty$, depending on the direction.

Would you like more details or have any questions? Here are some related questions to further explore:

1. How can we calculate the horizontal asymptote for any rational function?
2. What happens when $x$ approaches the asymptotes $x = 1$ or $x = 4$?
3. How can we find the domain of this function, considering the vertical asymptotes?
4. What are the critical points of the function where it changes concavity?
5. How do we find the intervals where this function is increasing or decreasing?

Tip: Vertical asymptotes occur where the denominator of a rational function equals zero, but the numerator doesn't.