SOLUTION: Write the absolute value equation that has a vertical reflection, shrunk horizontally by 1/2, vertically translated 3 units up and horizontally translated 2 units left

Question 1179841: Write the absolute value equation that has a vertical reflection, shrunk horizontally by 1/2, vertically translated 3 units up and horizontally translated 2 units left
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**Understanding Absolute Value Transformations**
The general form of an absolute value function is:
f(x) = a |b(x - h)| + k
where:
* **a:** Controls vertical reflection and stretch/shrink.
* If a is negative, there's a vertical reflection.
* |a| > 1: Vertical stretch
* 0 < |a| < 1: Vertical shrink
* **b:** Controls horizontal reflection and stretch/shrink.
* If b is negative, there's a horizontal reflection.
* |b| > 1: Horizontal shrink
* 0 < |b| < 1: Horizontal stretch
* **h:** Horizontal shift (left or right).
* (x - h): Shifts the graph h units to the right.
* (x + h): Shifts the graph h units to the left.
* **k:** Vertical shift (up or down).
* +k: Shifts the graph k units up.
* -k: Shifts the graph k units down.
**Applying the Given Transformations**
1. **Vertical Reflection:** a = -1
2. **Horizontal Shrink by 1/2:** b = 2
3. **Vertical Translation 3 Units Up:** k = 3
4. **Horizontal Translation 2 Units Left:** h = -2
**Substituting the Values**
f(x) = -1 |2(x - (-2))| + 3
**Simplified Equation**
f(x) = - |2(x + 2)| + 3

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