Question
What are the domain and range of y = -2(x-4)² + 1? A. D: x > 4 and R: all real numbers B. D: x ≤ 4 and R: all real numbers C. D: all real numbers and R: y ≤ 1 D. D: all real numbers and R: y ≥ 1
Answer
D. D: all real numbers and R: y ≤ 1
- Q: What is the equation of the given function? A: The equation of the function is y = -2(x-4)² + 1.
- Q: What is the vertex form of the equation? A: The vertex form of the equation is y=a(x-h)²+k, where (h,k) is the vertex of the parabola.
- Q: What is the vertex of the parabola? A: The vertex of the parabola is (4,1), so (h,k)=(4,1).
- Q: What is the shape of the parabola? A: Since the coefficient of the squared term is negative, the parabola opens downwards.
- Q: What is the domain? A: The domain is all real numbers, since there are no restrictions on the value of x.
- Q: What is the range? A: The maximum value of y is 1, which occurs at the vertex. Therefore, the range is y ≤ 1.