1. The problem states that the point $(1,4)$ lies on the graph of $f(x)$, meaning $f(1) = 4$. 2. We want to find which point lies on the graph of $y = f(x) + 3$. 3. The function $y = f(x) + 3$ shifts the graph of $f(x)$ vertically upward by 3 units. 4. Since $f(1) = 4$, then $y = f(1) + 3 = 4 + 3 = 7$. 5. Therefore, the point on the graph of $y = f(x) + 3$ corresponding to $x=1$ is $(1,7)$. 6. Checking the options, $(1,7)$ is the correct point on the graph of $y = f(x) + 3$. Final answer: $(1,7)$