Step 1: Split the plot into two frequency zones.
Below $\omega_0$ the line falls with slope $-20$ dB/decade. Above $\omega_0$ it sits flat at $0$ dB.
Step 2: Match the low-frequency zone to a building block.
A term like $\dfrac{1}{s/\omega_0}$ has magnitude $\omega_0/\omega$, which falls at $-20$ dB/decade, exactly the shape seen for $\omega<\omega_0$. This tells us the denominator must contribute a bare $s/\omega_0$ term.
Step 3: Match the high-frequency zone to a building block.
For the plot to flatten out at $0$ dB above $\omega_0$, the transfer function must approach $1$ as $\omega\to\infty$. A numerator of $1+s/\omega_0$ paired with the same $s/\omega_0$ in the denominator does exactly this, since both terms are dominated by $s/\omega_0$ at high frequency and cancel to $1$.
Step 4: Assemble the transfer function.
\[ G(s)=\frac{1+\dfrac{s}{\omega_0}}{\dfrac{s}{\omega_0}} \]
Step 5: Check the corner frequency.
At $s=j\omega_0$, the numerator gives $|1+j1|=\sqrt2$ and the denominator gives $|j1|=1$, so the curve bends near $\omega_0$ exactly where the plot shows the kink, confirming this is the right match, while the sign-flipped options (C) and (D) describe unstable, non-minimum-phase systems that are not what a simple asymptotic sketch is used to represent.
\[ \boxed{G(s)=\dfrac{1+\dfrac{s}{\omega_0}}{\dfrac{s}{\omega_0}}} \]
