Question

Transform the function f(x) = x² to g(x) = -(x - 1)².

a) g(x) = -x² + 2x - 1
b) g(x) = -x² - 2x + 1
c) g(x) = -x² + 2x + 1
d) g(x) = -x² - 2x - 1

Answer 1

After expanding and simplifying the function g(x) = -(x - 1)², we find that the correct transformation is g(x) = -x² + 2x - 1, which corresponds to option (a).

Step-by-step explanation:

The question asks for the transformation of the function f(x) = x² to g(x) = -(x - 1)². To find the correct transformation, we will expand the equation g(x) and then simplify:

• First, expand the squared term: (x - 1)² = x² - 2x · 1 + 1² = x² - 2x + 1
• Next, apply the negative sign to all terms: g(x) = -x² + 2x - 1

This matches option (a), therefore the correct transformation of the function is g(x) = -x² + 2x - 1.