16. $$ f(x)=2 x+6 $$, vertical shrink by a factor of $$ \frac{1}{2} $$

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To apply a **vertical shrink by a factor of $$ \frac{1}{2} $$** to the function $$ f(x) = 2x + 6 $$, you multiply the entire function by $$ \frac{1}{2} $$.

Here's how it's done step-by-step:

1. **Original Function:**
   $$
   f(x) = 2x + 6
   $$

2. **Apply Vertical Shrink:**
   Multiply the function by $$ \frac{1}{2} $$:
   $$
   g(x) = \frac{1}{2} \cdot f(x) = \frac{1}{2}(2x + 6)
   $$

3. **Simplify:**
   $$
   g(x) = \frac{1}{2} \cdot 2x + \frac{1}{2} \cdot 6 = x + 3
   $$

**Transformed Function:**
$$
g(x) = x + 3
$$

**Summary:**
- **Original Function:** $$ f(x) = 2x + 6 $$
- **After Vertical Shrink by $$ \frac{1}{2} $$:** $$ g(x) = x + 3 $$

This transformation compresses the graph of $$ f(x) $$ vertically by reducing its slope from 2 to 1, effectively making the graph less steep.
After applying a vertical shrink by a factor of $$ \frac{1}{2} $$ to the function $$ f(x) = 2x + 6 $$, the transformed function becomes $$ g(x) = x + 3 $$.

16. \( f(x)=2 x+6 \), vertical shrink by a factor of \( \frac{1}{2} \)

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