Answer
(a) See below.
(b) Domain: $(-\infty, \infty)$
Range:$[-8, \infty)$
(c) Domain where function decreases:$(-\infty, 1]$
Domain where function increases: $[1, \infty)$
Work Step by Step
First, we convert to vertex form to find the range and increasing and decreasing domains easier:
$f(x)=x^2-2x-8$
$f(x)=x^2-2x+1-8-1$
$f(x)=(x-1)^2-9$
Recap:
The domain is a horizontal span from the function's smallest value of x to the function's largest value of x.
The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x).
A function is increasing in the domain intervals where its slope is positive. On the other hand, a function is decreasing in the domain intervals where its slope is negative. In a quadratic function, we can find where the function starts or stops increasing by locating the vertex.