Answer: B. $(0,\dfrac{1}{9})$

Explanation:1. Understand the y-intercept: The y-intercept of a graph is the point where the graph crosses the y-axis. This occurs when $x=0$. To find the y-coordinate of the y-intercept, we substitute $x=0$ into the function.

2. Substitute $x=0$ into the given function $g(x)$: $g(0) = \dfrac{1}{9}(5)^0$

3. Evaluate the expression: Any non-zero number raised to the power of $0$ is $1$. So, $5^0 = 1$. $g(0) = \dfrac{1}{9}(1)$ $g(0) = \dfrac{1}{9}$

4. State the y-intercept as a point: The y-intercept occurs at $x=0$ and $y = g(0) = \dfrac{1}{9}$. So, the y-intercept is the point $(0, \dfrac{1}{9})$.

5. Check the solution with the options: Option [B] is $(0,\dfrac{1}{9})$, which matches our result.

6. Conclusion: The y-intercept of the graph of $g(x)$ is $(0,\dfrac{1}{9})$.