1. The problem asks us to find the equation of a function $g(x)$ that shifts the graph of $f(x) = \frac{1}{x}$ left by 2 units and up by 4 units. 2. The general rule for shifting a function $f(x)$ is: - Shift left by $h$ units: replace $x$ with $x + h$ in the function. - Shift up by $k$ units: add $k$ to the function. 3. Applying these rules to $f(x) = \frac{1}{x}$: - Shift left 2 units: replace $x$ with $x + 2$, so the function becomes $\frac{1}{x + 2}$. - Shift up 4 units: add 4 to the function, so it becomes $\frac{1}{x + 2} + 4$. 4. Therefore, the equation of $g(x)$ is: $$g(x) = \frac{1}{x + 2} + 4$$ This function represents the graph of $f(x)$ shifted left by 2 units and up by 4 units.