Final answer:
The graph of f(x) = |1/2x - 2| + 3 has been vertically stretched, horizontally shifted right by 4 units, and vertically shifted up by 3 units from its parent function f(x) = |x|.
Step-by-step explanation:
To explore how the graph of the function f(x) = |1/2x - 2| + 3 relates to the graph of its parent function, we should first identify what the parent function is. The parent function in this case is f(x) = |x|, which is the absolute value function. The transformation includes a vertical stretch by a factor of 1/2, a horizontal translation 4 units to the right, and a vertical translation 3 units up.
The graph of f(x) = |1/2x - 2| + 3 will have a V-shape like the parent function, but it will be narrower due to the vertical stretch. The lowest point of the V (the vertex) is shifted from the origin to the point (4, 3) due to the horizontal and vertical translations.
When plotting f(x), it's important to label the x and y axes, use an appropriate scale, and identify key points of the graph to compare it accurately to the parent function's graph.