Final answer:
To evaluate f(x) = x² - 5x + 1, substitute the given values into the function: f(0) = 1, f(-6) = 67, and f(4) = -3.
Step-by-step explanation:
To evaluate the function f(x) = x² - 5x + 1 at given values of x, we substitute these values into the function and perform the necessary calculations.
- f(0): Substitute x = 0 into the function to get f(0) = 0² - 5(0) + 1, which simplifies to f(0) = 1.
- f(-6): Substitute x = -6 into the function to get f(-6) = (-6)² - 5(-6) + 1, which simplifies to f(-6) = 36 + 30 + 1, giving f(-6) = 67.
- f(4): Substitute x = 4 into the function to get f(4) = 4² - 5(4) + 1, which simplifies to f(4) = 16 - 20 + 1, yielding f(4) = -3.