The diagram shows the graph of a function - HSC - SSCE Mathematics Extension 1 - Question 8 - 2023 - Paper 1

To determine the correct equation of the function from the given choices, we will analyze how the absolute value affects the graph based on the structure of the function.

1. Choice A: $y = |1 - ||x - 2||$

   • This equation will create a reflection based on the inner expression $||x - 2||$ and then shift it up by 1. It does not correspond with the peaks and valleys observed on the graph.

2. Choice B: $y = |2 - ||x - 1||$

   • Similar to choice A, this expression reflects around a different center (1), and does not match the graphical representation since it would create a different pattern.

3. Choice C: $y = |1 - |x - 2|$

   • This function centers at $x = 2$ but translates downward as $y$ increases. Upon evaluation, it produces correct peaks at the expected points.

4. Choice D: $y = |2 - |x - 1|$

   • It reflects appropriately but does not have the necessary characteristics to match the graph when evaluated for $x$ values, leading to a mismatch.

After evaluating each choice based on the structure and the expected outputs mentioned, we conclude that the correct function that corresponds to the graph is found in Choice C.