To translate the graph of $f(x) = |2x|$ 5 units to the left, we modify the function by adjusting the input $x$ in the absolute value expression. Translating to the left by 5 units means we replace $x$ with $x + 5$ in the function.

Thus, the transformed function becomes: $g(x) = |2(x + 5)|$

Answer

The correct choice is: $g(x) = |2(x + 5)|$

Would you like further explanation on translations, or do you have any questions?

Here are five related questions to expand your understanding:

1. How would the function $f(x) = |2x|$ change if it were translated 5 units to the right instead?
2. What would happen to $f(x) = |2x|$ if it were translated 5 units up instead of to the left?
3. How does the graph of $f(x) = |2x|$ compare to the graph of $f(x) = |x|$ in terms of steepness?
4. What transformation occurs if you replace $x$ with $-x$ in $f(x) = |2x|$?
5. How do we interpret a vertical stretch or compression in terms of absolute value functions?

Tip: Remember that horizontal translations in a function $f(x)$ can be made by adding or subtracting from the input $x$, where $x + a$ shifts the graph left, and $x - a$ shifts it right.