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To translate the graph of $y=f(x)$ four units left and three units down, replace $x$ with $x+4$ inside the function argument and subtract 3 outside the function. The final transformed equation is $y=f(x+4)-3$.

Conditions: The starting graph has equation $y=f(x)$.; The intended transformation is a horizontal translation 4 units left and a vertical translation 3 units down.

To translate the graph of $y=f(x)$ four units left and three units down, replace $x$ with $x+4$ inside the function argument and subtract 3 outside the function. The final transformed equation is $y=f(x+4)-3$.

Conditions: The starting graph has equation $y=f(x)$.; The intended transformation is a horizontal translation 4 units left and a vertical translation 3 units down.