What is the range of the function f(x) = -(x + 3)2 + 7?
Solution:
Given, the function is f(x) = -(x + 3)² + 7 ---------------- (1)
We have to find the range of the function.
The equation of a parabola in vertex form is given by
y = a|x - h| + k ----------------- (2)
Where (h, k) is the vertex
Comparing (1) and (2),
h = -3
k = 7
So, the vertex would be (-3, 7).
The range of the function is the set of y values for which the function is defined.
The given function has a vertex (-3, 7), it would not take any values which are greater than 7.
The range would be all y values less than or equal to 7.
Therefore, range is given by {y|y ≤ 7}
What is the range of the function f(x) = -(x + 3)2 + 7?
Summary:
The range of the function f(x) = -(x + 3)² + 7 would be all y values less than or equal to 7.