To solve this problem, we need to shift the graph of $f(x) = 2|x|$ right by 5 units.

When shifting a function $f(x)$ horizontally:

• To shift right by $c$ units, replace $x$ with $x - c$ in the function.
• Therefore, the equation becomes: $g(x) = 2|x - 5|$

Thus, the function $g(x)$ that shifts $f(x)$ to the right by 5 units is: $g(x) = 2|x - 5|$

Let me know if you’d like me to provide additional explanations or visualizations of this transformation.

5 Related Questions:

1. How would you shift the graph $f(x) = 2|x|$ left by 3 units? What would the equation be?
2. What happens if you shift the function $f(x) = 2|x|$ upward by 4 units?
3. How do vertical stretches or compressions affect the graph of an absolute value function?
4. How would you write the equation for shifting $f(x) = 2|x|$ both right by 5 units and upward by 3 units?
5. What is the effect of replacing $|x|$ with $|x + c|$ versus $|x - c|$?

Tip:

To confirm your graph transformations, try substituting key points from the original graph into the transformed equation to check if the new graph shifts correctly.