Final Answer:
The equation 16x - y² = 0 can be written as a function for y in the form B. y = -√(16x).
Step-by-step explanation:
To express the given equation 16x - y² = 0 as a function for y, we need to isolate y. Starting with the original equation, we add y² to both sides and then take the square root of both sides to solve for y. This yields y = ±√(16x). However, we choose the negative square root because the original equation has y², and we want to maintain the negative sign, making the correct function y = -√(16x).
To verify this, we can square both sides of the obtained function to confirm that it satisfies the original equation. Squaring -√(16x) gives 16x - (-√(16x))² = 16x - 16x = 0, which aligns with the original equation 16x - y² = 0. Therefore, the correct function for y is y = -√(16x), corresponding to option B.
In conclusion, by carefully manipulating the given equation and considering the square root, we arrive at the correct function y = -√(16x), ensuring that it satisfies the original equation 16x - y² = 0.