通过将曲线方程 $y = \frac{12x + 11}{2x + 1}$ 表示为 $y = A + \frac{B}{2x + 1}$ 的形式（其中 $A$ 和 $B$ 是常数），描述一个由三个变换组成的序列，该序列将 $y = \frac{1}{2x - 3}$ 的图像映射到 $y = \frac{12x + 11}{2x + 1}$ 的图像上。 图中显示了 $y = \mathrm{f}(x)$ 的图像。该曲线在 $(0, -5)$ 处有一个极大值点，在 $(6, -4)$ 处有一个极小值点。曲线的渐近线方程为 $x = -2$，$x = 2$ 和 $y = -2$。 画出 $y = \mathrm{f}(-x + 2) + 4$ 的草图，清晰标出渐近线的方程以及与坐标轴交点和极值点的坐标。

1. Express the given equation in the required partial fraction form to identify constants $A$ and $B$.

$y = \frac{12x + 11}{2x + 1}$
$y = \frac{6(2x + 1) + 5}{2x + 1}$
$y = 6 + \frac{5}{2x + 1}$
Thus, $A = 6$ and $B = 5$.

2. Determine the horizontal translation required to transform the denominator.

We start with the original curve $\mathrm{f}(x) = \frac{1}{2x - 3}$.
To change the denominator to $2x + 1$, we need to replace $x$ with $x + 2$:
$\mathrm{f}(x + 2) = \frac{1}{2(x + 2) - 3} = \frac{1}{2x + 1}$
This corresponds to a translation of $-2$ units parallel to the $x$-axis.

3. Determine the vertical scaling required to match the numerator.

Next, we multiply the function by $5$ to get the required numerator of $B = 5$:
$5\mathrm{f}(x + 2) = \frac{5}{2x + 1}$
This corresponds to a scaling parallel to the $y$-axis with a scale factor of $5$.

4. Determine the vertical translation required to complete the function mapping.

Finally, we add $6$ to the function to account for $A = 6$:
$5\mathrm{f}(x + 2) + 6 = 6 + \frac{5}{2x + 1}$
This corresponds to a translation of $6$ units parallel to the $y$-axis.