Write a absolute value function that has been reflected across the x-axis, shrunk by 3/8
 
, shifted right by 4, and shifted down by 1.

To construct an absolute value function that satisfies the given transformations, follow these steps:

1. **Reflection across the x-axis**: The function is multiplied by \(-1\).
2. **Vertical shrink by 3/8**: Multiply the function by \( \frac{3}{8} \).
3. **Shift right by 4**: Replace \(x\) with \(x - 4\) inside the absolute value.
4. **Shift down by 1**: Subtract 1 from the entire function.

Now, starting with the general absolute value function \( f(x) = |x| \), applying these transformations gives the following function:

\[
f(x) = -\frac{3}{8} |x - 4| - 1
\]

### Breakdown of the function:
- The \(-\) reflects the graph across the x-axis.
- The \( \frac{3}{8} \) shrinks the graph vertically by a factor of 3/8.
- The \( x - 4 \) shifts the graph 4 units to the right.
- The \(-1\) shifts the graph 1 unit down.

Would you like more details on how these transformations work, or do you have any questions?

### Related questions:
1. What is the effect of reflecting an absolute value function across the y-axis?
2. How do horizontal stretches affect absolute value functions?
3. What is the role of the absolute value in real-world applications?
4. Can you explain how to graph the function \( -\frac{3}{8} |x - 4| - 1 \) step by step?
5. What happens if the function is stretched instead of shrunk vertically?

**Tip**: Always apply horizontal transformations before vertical transformations when graphing functions!

Write an absolute value function that has been reflected across the x-axis, shrunk by 3/8, shifted right by 4, and shifted down by 1.

Learn how to create and graph an absolute value function that is reflected across the x-axis, vertically shrunk by 3/8, shifted 4 units to the right, and shifted 1 unit down. This example covers key algebraic transformations for students in Grades 9-12.

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