The circuit above has two resistors in parallel. The first, $R_1$, will have its resistance steadily increased. The second, $R_2$, will have a constant resistance of $R_2= 4\Omega $. Which of the following graphs correctly depicts the total resistance of the circuit, $R_{\mathrm{T}}$, as a function of $R_1$?
For resistors in parallel, you know
$$\frac{1}{R_{\mathrm{T}}}=\frac{1}{R_1}+\frac{1}{R_2}$$
$$\frac{1}{R_{\mathrm{T}}}=\frac{R_2+R_1}{R_1R_2}$$
which means
$$R_{\mathrm{T}}=\frac{R_1R_2}{R_1+R_2}$$
You know $R_2=4\ \Omega $ so plug that in to get
$$R_{\mathrm{T}}=\frac{4R_1}{R_1+4}$$
The graph of this equation looks like $\mathrm{(B)}$. It will always be increasing, but it will increase more and more slowly.