The domain: -∞ < x < ∞
The range: g(x) ≥ -16
Explanation:The given function is:
[tex]g(x)\text{ = x}^2\text{-2x-15}[/tex]The domain is a set of all the valid inputs that can make the function real
All real values of x will make the function g(x) to be valid
The domain: -∞ < x < ∞
The range is the set of all valid outputs
From the function g(x):
a = 1, b = -2
[tex]\begin{gathered} \frac{b}{2a}=\frac{-2}{2(1)}=-1 \\ g(-1)=(-1)^2-2(-1)-15 \\ g(-1)=1-2-15 \\ g(-1)=-16 \end{gathered}[/tex]Since a is positive, the graph will open upwards
Therefore, the range of the function g(x) is: g(x) ≥ -16
The graph of the function g(x) = x^2 - 2x - 15 is plotted below
