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.