Final answer:
The parent function f(x) = |x| can be transformed by shifting horizontally, vertically, and stretching or compressing the graph.
Step-by-step explanation:
The parent function f(x) = |x| represents the absolute value function. When considering transformations of this function, we can use the general form y = a |x - h| + k, where (h, k) represents the vertex of the graph and a determines the stretch or compression of the graph.
If a > 1, the graph is compressed horizontally. If 0 < a < 1, the graph is stretched horizontally. If a is negative, the graph is reflected in the x-axis.
For example, if we have the transformation f(x) = 2 |x - 3| + 1, the graph is compressed horizontally by a factor of 2, shifted 3 units to the right, and shifted 1 unit upward.