Answer each of the following questions about the graph for 
 
   y=4/11|x-7|-2

1. Does the graph open up or down? 
Select an answer


2. Give the vertex as an ordered pair. 


3. Is this point the maximum or minimum of the graph? 
Select an answer


4. Is the graph wider, narrower, or the same width as the parent function 
? 
Select an answer


5. From the parent fucntion 
 this graph has been shift horizontally 
?
 unit(s) to the 
Select an answer


6. From the parent function 
 this graph has been shifted vertically 
?
 unit(s) 
Select an answer
 .

Let's break down the equation step by step:

Given equation: 

\[
y = \frac{4}{11} |x - 7| - 2
\]

1. **Does the graph open up or down?**
   - The coefficient of the absolute value function, \( \frac{4}{11} \), is positive. This means the graph opens *up*.

   **Answer:** The graph opens *up*.

2. **Give the vertex as an ordered pair.**
   - The general form of the absolute value function is \( y = a|x-h| + k \), where the vertex is at \( (h, k) \).
   - In this case, the vertex is at \( (7, -2) \).

   **Answer:** The vertex is \( (7, -2) \).

3. **Is this point the maximum or minimum of the graph?**
   - Since the graph opens upwards, the vertex represents the *minimum* point of the graph.

   **Answer:** This point is the *minimum*.

4. **Is the graph wider, narrower, or the same width as the parent function \( y = |x| \)?**
   - The coefficient \( \frac{4}{11} \) is less than 1, which means the graph is *wider* than the parent function.

   **Answer:** The graph is *wider*.

5. **From the parent function \( y = |x| \), this graph has been shifted horizontally how many unit(s) to the left or right?**
   - The term \( |x - 7| \) indicates a horizontal shift 7 units to the *right*.

   **Answer:** 7 units to the *right*.

6. **From the parent function \( y = |x| \), this graph has been shifted vertically how many unit(s)?**
   - The \( -2 \) outside the absolute value indicates a vertical shift 2 units *down*.

   **Answer:** 2 units *down*.

### Relative Questions:
1. How would the graph change if the coefficient of the absolute value were negative?
2. What is the effect of increasing the coefficient of \( |x-7| \)?
3. How does the vertex form help identify transformations of the parent function?
4. If the horizontal shift were 5 units to the left, what would the equation look like?
5. How would the graph change if the vertical shift was 3 units up?

### Tip:
When dealing with absolute value functions, always check the sign of the coefficient in front of the absolute value to determine the direction of the opening.

Answer each of the following questions about the graph for y = 4/11|x - 7| - 2:

1. Does the graph open up or down?
2. Give the vertex as an ordered pair.
3. Is this point the maximum or minimum of the graph?
4. Is the graph wider, narrower, or the same width as the parent function?
5. From the parent function, this graph has been shifted horizontally how many unit(s) to the left or right?
6. From the parent function, this graph has been shifted vertically how many unit(s)?

Explore how to graph and transform the absolute value function y = 4/11|x - 7| - 2, including identifying the vertex, determining whether the graph opens up or down, and understanding the shifts and changes in width. Suitable for students in Grades 9-11.

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