https://file.aiquickdraw.com/mathbot/file/1729601629634qq5s7q9o.jpg

The graph displayed shows a transformation of the absolute value function \( f(x) = |x| \). Based on the graph, we can observe that the vertex of the graph is at the point \( (0, 2) \) instead of the origin \( (0, 0) \), which indicates a vertical shift of the absolute value function by 2 units upwards. Additionally, the slope of the lines on both sides appears to be unchanged from the standard \( f(x) = |x| \).

Therefore, the transformation rule for \( g(x) \) would be:
\[
g(x) = |x| + 2
\]
This represents a vertical translation of the parent function \( f(x) = |x| \) by 2 units upwards.

Would you like more details or explanations? 

Here are some related questions for further practice:

1. What would the function look like if there was a horizontal shift to the right by 3 units?
2. How does a reflection over the x-axis affect the function rule for \( f(x) = |x| \)?
3. If the graph was stretched vertically by a factor of 2, what would the function rule be?
4. How would the function rule change if the graph was shifted 4 units down?
5. What is the effect of shifting the graph both vertically and horizontally?

**Tip:** Vertical shifts affect only the constant term in the absolute value function, while horizontal shifts modify the variable inside the absolute value symbol.

The graph shows g(x), which is a transformation of f(x) = |x|. Write the function rule for g(x).

Understand how to transform the absolute value function f(x) = |x| into g(x) = |x| + 2 by applying a vertical shift. Learn about transformations and translations of functions in this algebraic concept, suitable for students in Grades 9-11.

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