Final answer:
To obtain the graph of f(x) = |x| reflected across the x-axis, translated 2 units down, and 1 unit to the left, you need to apply the transformations step by step. First, reflect the function across the x-axis by taking the negative. Then, translate it 2 units down by subtracting 2. Finally, translate it 1 unit to the left by replacing x with (x + 1) in the function.
Step-by-step explanation:
The graph of f(x) = |x| reflected across the x-axis, translated 2 units down and 1 unit to the left can be obtained by applying the transformations step by step.
- Reflected across the x-axis: This is achieved by taking the negative of the original function. Since f(x) = |x|, the reflected function is f(x) = -|x|.
- Translated 2 units down: This is done by subtracting 2 from the function. So, the new function becomes f(x) = -|x| - 2.
- Translated 1 unit to the left: This is achieved by replacing x with (x + 1) in the function. So, the final function is f(x) = -|x + 1| - 2.
Therefore, the graph that shows f(x) = |x| reflected across the x-axis, translated 2 units down, and 1 unit to the left is represented by the function f(x) = -|x + 1| - 2.