Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function $$ f(x)=|x| $$. $$ y=|x-4|+3 $$ The vertex is $$ \square $$. (Type an ordered pair.)

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For the function $$ y = |x - 4| + 3 $$:

- **Vertex:** The vertex of the function is $$ (4,\, 3) $$.

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**Explanation:**

The general form of a transformed absolute value function is:
$$ y = |x - h| + k $$
where:
- $$ (h, k) $$ is the **vertex** of the graph.
- The graph is shifted $$ h $$ units **horizontally** and $$ k $$ units **vertically** from the parent function $$ f(x) = |x| $$.

For the given function $$ y = |x - 4| + 3 $$:
- $$ h = 4 $$ (horizontal shift to the right by 4 units)
- $$ k = 3 $$ (vertical shift upward by 3 units)

Therefore, the **vertex** is located at $$ (4, 3) $$.

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**Additional Details:**

- **Axis of Symmetry:** The axis of symmetry for the function is the vertical line that passes through the vertex. For this function, it is:
  $$ x = 4 $$

- **Transformations from the Parent Function $$ f(x) = |x| $$:**
  1. **Horizontal Shift:** The graph is shifted **4 units to the right** due to the $$ (x - 4) $$ inside the absolute value.
  2. **Vertical Shift:** The graph is shifted **3 units upward** due to the $$ +3 $$ outside the absolute value.

These transformations result in the vertex moving from the origin $$ (0, 0) $$ in the parent function to $$ (4, 3) $$ in the transformed function.
The vertex is $$ (4, 3) $$.

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function \( f(x)=|x| \). \( y=|x-4|+3 \) The vertex is \( \square \). (Type an ordered pair.)

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