https://file.aiquickdraw.com/mathbot/file/1729684949120kr1k6wbf.jpg

From the image, I can see two functions represented graphically: one in red (labeled \( g \)) and one in green (labeled \( f \)). Both functions appear to be piecewise linear (V-shaped). Let's determine their equations step by step:

### 1. Function \( g(x) \) (Red Graph):
- The graph of \( g(x) \) is a V-shaped absolute value function centered at \( x = -1 \). 
- The slopes are negative to the left and positive to the right of \( x = -1 \), indicating it's of the form:
  \[
  g(x) = |x + 1|
  \]
  This translates to a shift of the basic absolute value function \( |x| \) to the left by 1 unit.

### 2. Function \( f(x) \) (Green Graph):
- The graph of \( f(x) \) is also a V-shaped function, but it's centered at \( x = 3 \).
- The slopes are similar to those of \( g(x) \), indicating a standard absolute value function shifted to the right by 3 units. So:
  \[
  f(x) = |x - 3|
  \]
  
Thus, the two functions are:
- \( g(x) = |x + 1| \)
- \( f(x) = |x - 3| \)

Would you like to dive deeper into these functions or ask questions about them? Here are some related questions you can explore:

1. What happens to the graph if we multiply the absolute value function by a constant?
2. How would the graph change if the absolute value function was translated vertically?
3. What is the domain and range of each function \( f(x) \) and \( g(x) \)?
4. Can you find the intersection points of the two functions graphically or algebraically?
5. How would you write the piecewise definition for each function?

**Tip**: To transform absolute value functions, shifts to the left or right affect the inside of the absolute value, while vertical shifts affect the whole function.

Discover how to find the equations of two absolute value functions, g(x) = |x + 1| and f(x) = |x - 3|, from a graph. This problem covers key algebraic concepts, such as piecewise and absolute value functions, and is ideal for students in Grades 8-10.

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