Question

Which transformation reflects f(x) = (x - 1)² + 1 over the x-axis?

a) f'(x) = (-2x - 1)² + 1
b) f'(x) = -1.4((x - 1)² + 1)
c) f'(x) = 0.1((x - 1)² + 1)
d) f'(x) = (0.5x - 1)² + 1

Answer 1

Option b, f'(x) = -1.4((x - 1)² + 1), correctly represents the reflection of the function f(x) = (x - 1)² + 1 over the x-axis, even though the multiplication factor is -1.4 instead of -1.

Step-by-step explanation:

The question asks which transformation reflects the function f(x) = (x - 1)² + 1 over the x-axis. Reflecting a function over the x-axis means to multiply the function's output by -1. Therefore, the reflected function f'(x) would be represented by multiplying the original function by -1, which yields f'(x) = -(x - 1)² - 1.

Among the provided options, this means option b is correct, as it reflects the function over the x-axis by multiplying the entire function by -1.