https://file.aiquickdraw.com/mathbot/file/17256765076903y3mu9xn.jpg

Let's analyze the image you provided.

From what I can see:

1. The graph shows two functions:
   - The red line labeled \( g(x) \)
   - The blue line labeled \( f(x) = |x| \), which is the standard absolute value function.

2. The goal is to find the formula for \( g(x) \).

### Observations:
- The blue graph is \( f(x) = |x| \), which represents the V-shaped absolute value function.
- The red graph appears to be a transformation of the blue one. Specifically:
  - It has the same shape as \( |x| \), but it is translated vertically.
  
### Finding the formula for \( g(x) \):
- The red graph seems to be a vertical shift of \( f(x) = |x| \).
- Notice that the vertex of the red graph is at \( (0, 8) \) (instead of at \( (0, 0) \) for \( f(x) = |x| \)).
- This suggests a vertical shift of 8 units upward.

Therefore, the formula for \( g(x) \) is:
\[
g(x) = |x| + 8
\]

Would you like further details or have any questions?

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Here are some related questions to expand your understanding:
1. How do vertical shifts affect the equation of absolute value functions?
2. What changes would result in horizontal shifts for \( f(x) = |x| \)?
3. How would the equation of \( f(x) = |x| \) change if it were reflected across the x-axis?
4. Can you explain how scaling (compressing/stretching) affects the absolute value function?
5. What is the general form of transformations for the function \( f(x) = |x| \)?

**Tip**: When determining shifts and transformations of a graph, always compare the vertex and slope of key segments.

The graphs of f and g are given. Find a formula for the function g.

Learn how to find the formula for the function g(x) given its graph as a vertical shift of the standard absolute value function f(x) = |x|. This problem covers algebraic concepts related to graph transformations, suitable for students in Grades 9-11.

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