Final answer:
The base function for the given function g(x) = -2²(x-2)+4 is f(x) = -2(x-2)+4.
The answer is option ⇒2
Step-by-step explanation:
To find the base function, we need to simplify the given function by expanding and combining like terms. Let's go through the steps:
1. Start with the given function: g(x) = -2²(x-2)+4.
2. Square -2: (-2)² = (-2)(-2) = 4.
3. Rewrite the function with the squared value: g(x) = 4(x-2)+4.
4. Distribute 4 to both terms inside the parentheses: g(x) = 4x - 8 + 4.
5. Combine like terms: -8 + 4 = -4.
6. Simplify further: g(x) = 4x - 4.
After simplifying and rearranging, we get the base function as f(x) = -2(x-2)+4.
The answer is option ⇒2