Which describes how the parent function, $$ f(x)=|x| $$, is transformed to show the function $$ f(x)=0.1|x-3| $$ ? It is wider and shifted 3 units to the left. It is wider and shifted 3 units to the right. It is narrower and shifted 3 units to the left. It is narrower and shifted 3 units to the right.

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The transformation from the parent function $$ f(x) = |x| $$ to the function $$ f(x) = 0.1|x-3| $$ involves two key changes:

1. **Vertical Scaling (Widening):**
   - The coefficient $$ 0.1 $$ in front of the absolute value function compresses the graph vertically. However, from the perspective of the graph's appearance, this makes the "V" shape wider compared to the parent function.

2. **Horizontal Shift (Right Shift):**
   - The expression $$ |x - 3| $$ shifts the graph horizontally. Specifically, subtracting 3 inside the absolute value translates the graph **3 units to the right**.

Combining these transformations, the function $$ f(x) = 0.1|x-3| $$ is **wider** than the parent function and shifted **3 units to the right**.

**Correct Answer:**
It is wider and shifted 3 units to the right.
The function $$ f(x) = 0.1|x-3| $$ is wider and shifted 3 units to the right compared to the parent function $$ f(x) = |x| $$.

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