Final answer:
To evaluate the function f(x) = -2x² + 5 for different values of x, consider the two cases when x is less than -1 or greater than -1. Substitute the values of x into the respective equations and calculate f(-3), f(-2), f(-1), and f(0).
Step-by-step explanation:
To evaluate the function f(x) = -2x² + 5 for different values of x, we need to consider the two cases when x is less than -1 or greater than -1.
For x values less than -1, we substitute the value of x in the equation f(x) = -2x² + 5. So, f(-3) = -2(-3)² + 5 = -2(9) + 5 = -18 + 5 = -13. Similarly, f(-2) = -2(-2)² + 5 = -2(4) + 5 = -8 + 5 = -3, f(-1) = -2(-1)² + 5 = -2(1) + 5 = -2 + 5 = 3.
For x values greater than -1, we substitute the value of x in the equation f(x) = 4x - 8. So, f(0) = 4(0) - 8 = 0 - 8 = -8.