Answer:
The domain is all real numbers.
The range is {y|y ≤ 16}
Step-by-step explanation:
Given function,
[tex]f(x)=-x^2-2x+15[/tex]
[tex]f(x) = -x^2 - 2x + 15 + 1 - 1[/tex]
[tex]f(x) = -(x^2 + 2x + 1) + 16[/tex]
[tex]f(x) = -(x+1)^2 + 16[/tex]
Which a downward parabola,
∵ The vertex form of a parabola is [tex]f(x)=a(x-h)^2 + k[/tex]
Where, (h, k) is the vertex of the parabola,
Thus, the vertex of the above parabola = ( -1, 16 ),
Since, a downward parabola gives maximum output value on its vertex,
So, the range of the parabola = all real numbers less than equal to 16,
i.e. Range = {y|y ≤ 16},
Now, a parabola is a polynomial and a polynomial is defined for all real numbers,
Hence, Domain = All real numbers
