To create a function $g(x)$ that represents a reflection in the y-axis followed by a translation 3 units to the right of the graph of $f(x) = |x|$, we can follow these steps:

1. Reflect the graph in the y-axis:

Reflecting the function $f(x) = |x|$ in the y-axis results in the function $f(-x) = |-x| = |x|$. Since $|x|$ is an even function, reflecting it over the y-axis does not change its appearance. So after the reflection, the function is still $|x|$.

2. Translate the graph 3 units to the right:

To translate the graph 3 units to the right, replace $x$ in the function with $x - 3$. Thus, the translated function is $f(x - 3) = |x - 3|$.

Final Function:

The final function $g(x)$ is: $g(x) = |x - 3|$

This function represents the graph of $f(x) = |x|$ reflected in the y-axis and then translated 3 units to the right.

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Do you want more details or have any questions?

Here are 5 related questions:

1. How would the graph of $f(x) = |x|$ change if reflected over the x-axis instead?
2. What would be the equation if the graph was translated 3 units to the left instead?
3. How does a vertical translation affect the function $f(x) = |x|$?
4. Can you describe the transformations needed to shift $f(x) = |x|$ 2 units down and 4 units to the left?
5. What is the effect of multiplying the function $f(x) = |x|$ by a negative constant?

Tip: When reflecting a function over the y-axis, always replace $x$ with $-x$ in the function.