\(f\) is a constant linear quadratic function, which means its natural domain is all real numbers.

Let’s factor. \(f(x) = -2 (x+4)(x-2)\)

The real zeros of \(f\), in numerical order, are

\(f\) is a constant linear quadratic function, which means it is continuous.

The leading coefficient of \(f\) is \(\answer {-2}\).

Because \(f\) is a quadratic function with a negative leading coefficient,

\(\lim \limits _{x \to -\infty } f(x) = \answer {-\infty }\)

\(\lim \limits _{x \to \infty } f(x) = \answer {-\infty }\)

Because \(f\) is a quadratic function with a negative leading coefficient, \(f\) increases on \(\left ( \answer {-\infty }, \answer {-1} \right ]\) and decreases on \(\left [ \answer {-1}, \answer {\infty } \right )\).

Because \(f\) increases on \(( -\infty , -1 ]\) and decreases on \([ -1, \infty )\), \(f\) has a global minimum maximum of \(\answer {18}\) at \(\answer {-1}\).

Because \(\lim \limits _{x \to \infty } f(x) = \answer {-\infty }\), \(f\) has no global minimum maximum.

The only local maximum value of \(f\) is the global maximum of \(\answer {18}\) at \(\answer {-1}\).

\(f\) is continuous with no minimum value and a maximum value of \(18\). Therefore, the range of \(f\) is