https://file.aiquickdraw.com/mathbot/file/1726453839848ea5oldym.jpg

Find a formula for each of the transformations whose graphs are given below.
Recall that absolute value is entered as abs.

From the graph you provided, it appears that the basic shape resembles the graph of an absolute value function. The standard form of an absolute value function is \( f(x) = |x| \), but the graph shows transformations such as shifts, stretches, or reflections.

Let's analyze the transformations:

1. **Reflection**: The graph is inverted compared to the basic absolute value function \( f(x) = |x| \). This indicates a reflection across the x-axis. So, the negative sign appears in front of the function: \( -|x| \).
  
2. **Vertical Stretch**: The sides of the "V" are steeper than the standard \( |x| \) graph. This indicates a vertical stretch by a factor of 4. So, the equation becomes \( -4|x| \).

3. **Translation**: The vertex is not at the origin but at \( (1, -4) \). This indicates a horizontal shift of 1 unit to the right and a vertical shift downward by 4 units.

Thus, the equation that represents the transformations is:

\[
f(x) = -4 |x - 1| - 4
\]

Would you like further clarification or additional details?

### Related Questions:
1. How do horizontal shifts affect the absolute value graph?
2. How would the graph change if the stretch factor were 2 instead of 4?
3. What would the equation look like without the vertical shift?
4. Can you explain how to graph absolute value transformations step by step?
5. How do reflections across the x-axis influence the graph of an absolute value function?

### Tip:
When analyzing transformations, always start with the base graph and apply each transformation (shift, stretch, reflection) one step at a time.

Find a formula for each of the transformations whose graphs are given below. Recall that absolute value is entered as abs.

This page explains how to find the transformation of an absolute value function based on the graph. The function f(x) = -4|x - 1| - 4 involves a reflection, vertical stretch, and translation. Suitable for Grades 9-11.

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