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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?

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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.

Which function represents the graph of f(x) = |2x| after it is translated 5 units to the left?

Learn how to translate the graph of the absolute value function f(x) = |2x| by 5 units to the left. This problem involves understanding function transformations and is ideal for high school students in Grades 9-12.

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