Let the utility function $U = a + b \min\{x,y\}$. Are $x$ and $y$ perfect complements? It is possible to have a monotonic transformation on this type of utility function, but what about $a$ and $b$? Usually a function with perfect complements is $U(x_1, x_2) = \min \{a x_1, b x_2 \}$
Consider a typical car, which is made of one car-body (for lack of a better word) and four tires. Let $x_1$ denote the number of car-bodies and $x_2$ denote the number of tires. Most consumers would prefer cars in the form of one car-body with four tires, and not in any other combinations. So we may represent their preference as 
$$U(x_1,x_2)=\min\{4x_1,x_2\}.\tag{1}$$
Thus two cars are preferred to one car can be expressed as 
$$
(2,8)\succ(1,4)\quad\Leftrightarrow\quad U(2,8)=8&gt;4=U(1,4). \tag{2}
$$
One car with two extra tires does not increase one's utility:
$$
(1,4)\sim(1,6)\quad\Leftrightarrow\quad U(1,4)=4=4=U(1,6).  \tag{3}
$$
Equation $(1)$ is the utility function associated with a perfect complement preference. In particular, it is a special case of the general form $\min\{ax_1,bx_2\}$ where $a=4$ and $b=1$. 

Let's now apply an affine positive transformation to $U(x_1,x_2)$. To avoid notational confusion, let's use $\alpha\in\mathbb R$ and $\beta&gt;0$ as the parameters:
$$
V(x_1,x_2)=\alpha+\beta U(x_1,x_2).
$$
For concreteness, suppose $\alpha=1$ and $\beta=0.5$. And we can verify that the preference illustrated in $(2)$ and $(3)$ is preserved:
$$
(2,8)\succ(1,4)\quad\Leftrightarrow\quad V(2,8)=5&gt;3=V(1,4). 
$$
$$
(1,4)\sim(1,6)\quad\Leftrightarrow\quad V(1,4)=3=3=V(1,6).  
$$

Therefore, while $\min\{ax_1,bx_2\}$ represents some perfect complement preference, its monotonic transformation, $\alpha+\beta\min\{ax_1,bx_2\}$, also represents the same preference.