we have
[tex]f(x)=-(x+3)^{2}+7[/tex]
we know that
The function is a vertical parabola open downward
The vertex is the point [tex](-3,7)[/tex]
The vertex is a maximum
The range is the interval-----------> (-∞,7]
That means
All real numbers less than or equal to [tex]7[/tex]
therefore
the answer is the option
All real numbers less than or equal to [tex]7[/tex]
The range of the function [tex]\rm f(x)= -(x + 3)^2 + 7[/tex] is ''all real numbers less than or equal to 7''.
Given
The function is;
[tex]\rm f(x)= -(x + 3)^2 + 7[/tex]
The range of the function f is the set of all images of the elements of the domain (or) the set of all the outputs of the function.
First, remember that range represents the y-values of the function.
f(x) =-(x + 3)² + 7 is in vertex form: a(x - h)² + k
Where (h, k) is the vertex.
The value of a is negative so it is reflected across the x-axis (upside-down parabola).
The parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity.
Hence, the range of the function [tex]\rm f(x)= -(x + 3)^2 + 7[/tex] is ''all real numbers less than or equal to 7''.
To know more about Range click the link given below.
https://brainly.com/question/13824428
