Final answer:
To match a function with its graph, analyze the transformations applied to the base absolute value function; horizontal shifts result from adding/subtracting within the absolute value, and vertical shifts occur when adding/subtracting outside the absolute value. Key points like the vertex help identify the correct function.
Step-by-step explanation:
To determine which function a graph represents, one must understand the effects that different operations have on the base function. In this case, we are concerned with transformations of the absolute value function, which is written as |x|. When we add or subtract a number to x within the absolute value function, it translates the graph horizontally. Adding moves it to the left while subtracting moves it to the right. Likewise, when we add or subtract a number outside the absolute value function, it translates the graph vertically.
Recall that the general form of the absolute value function translation is f(x) = |x - h| + k, where h shifts the graph horizontally and k shifts it vertically. For example, f(x) = |x + 5| - 1 would translate the base function 5 units to the left and 1 unit down.
To match a function to its graph, you would look for key points, such as the vertex of the absolute value function indicating horizontal shift, and then check the vertical displacement to determine the vertical translation. Without the specific graph mentioned in the student's question, it's impossible to provide the correct answer, but understanding these concepts will allow the student to match the graph to the correct function.