Final answer:
The transformation that shifts the function f(x) = (x - 5)² + 2 is Option C: f(x + 5) - 2, which translates the function 5 units to the left and 2 units downward.
Step-by-step explanation:
The question asks which transformation shifts the function f(x) = (x - 5)² + 2. This type of transformation is often referred to as a horizontal and vertical shift of the function's graph on the coordinate plane. To determine the correct transformation, we need to analyze how each of the given options would modify the original function
- Option A: f(x - 5) - 2 represents a translation of 5 units to the right and 2 units downward.
- Option B: f(x - 5) + 2 represents a translation of 5 units to the right and 2 units upward.
- Option C: f(x + 5) - 2 represents a translation of 5 units to the left and 2 units downward.
- Option D: f(x + 5) + 2 represents a translation of 5 units to the left and 2 units upward.
The original function is f(x) = (x - 5)² + 2, and we are looking for a transformation that shifts it without changing its shape. Using what we've learned about shifts, we can see that Option C f(x + 5) - 2 is the correct transformation. It horizontally shifts the function by 5 units to the left (adding 5 to x) and vertically shifts it down by 2 units (subtracting 2).