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The graph provided shows two functions, \( f(x) \) and \( g(x) \). Let's analyze the options to identify the parent function for \( g(x) \):

- The graph of \( g(x) \) has a V-shape, which is characteristic of the absolute value function.
- The absolute value function \( y = |x| \) produces a graph that is symmetric with respect to the y-axis, forming two linear pieces with different slopes for positive and negative values of \( x \).

Given that the shape of \( g(x) \) matches this description, the correct parent function is:

**A) \( y = |x| \)**.

Would you like more details or have any questions about this? Here are some related questions you might find interesting:

1. What transformations would shift the graph of \( g(x) \) horizontally?
2. How do transformations affect the graph of \( y = |x| \)?
3. What is the difference between the graphs of \( y = |x| \) and \( y = x^2 \)?
4. How does the graph of \( y = |x| \) change when it is reflected over the x-axis?
5. What are some real-world applications of absolute value functions?

**Tip:** When identifying parent functions, always look at the overall shape of the graph first—this often gives away the correct type of function!

Use the graph of the transformed function g(x) to identify the parent function. Select the correct parent function.

This problem involves using the graph of the function g(x) to identify the parent function. By recognizing the V-shaped graph, we conclude that the parent function is the absolute value function y = |x|. This problem covers core algebra concepts and is suitable for students in Grades 8-10.

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