Question 25 REASONING Compare the graph of the parent function \( f(x)=|x| \) with the graphs of \( g(x)=|x+2| \) and \( h(x)=|x-3| \). How are the graphs similar? How are they different? All of the graphs have a Select Choice \( v \) shape. The graph of \( g(x) \) is the graph of the parent function \( f(x) \) translated Select Choice 2 units, and that the graph of \( h(x) \) is the graph of \( f(x) \) translated Select Choice 3 units.

To compare the graphs of the functions \( f(x) = |x| \), \( g(x) = |x + 2| \), and \( h(x) = |x - 3| \), we can analyze their similarities and differences. ### Similarities: 1. **Shape**: All of the graphs have a "V" shape, characteristic of absolute value functions. This means they all open upwards and have a vertex point. 2. **Basic Structure**: Each function is based on the parent function \( f(x) = |x| \), which means they all exhibit the same basic behavior of being non-negative and symmetric about the y-axis. ### Differences: 1. **Vertex Location**: - The vertex of the parent function \( f(x) = |x| \) is at the origin (0, 0). - The graph of \( g(x) = |x + 2| \) is the graph of \( f(x) \) translated **2 units to the left**. This means its vertex is at (-2, 0). - The graph of \( h(x) = |x - 3| \) is the graph of \( f(x) \) translated **3 units to the right**. This means its vertex is at (3, 0). ### Summary: - All graphs have a "V" shape. - The graph of \( g(x) \) is the graph of the parent function \( f(x) \) translated **2 units to the left**. - The graph of \( h(x) \) is the graph of \( f(x) \) translated **3 units to the right**. This analysis highlights both the common characteristics of absolute value functions and the specific transformations that affect their positions on the graph.