and answer the following questions:
- Determine the interval(s) where the function f(x) is increasing? is decreasing?
- Determine the relative minimum and maximum values of the function.
- Determine all the intercepts.
- Determine whether f(x) is an odd function, an even function, or neither.
Answers: The function is even, its four x-intercepts are at x=-3, x=-2, x=2 and x=3. The function is increasing on the intervals 
and on 
, the function is decreasing on the intervals 
and on 
. The maximum value is 36, attained at x=0; the minimum value is -6.25, attained at 
.
- Find an equation for the circle passing through the point B centered at A.
- Is point C inside or outside of this circle? Prove your answer.
Answers: An equation of the circle is
The point C lies outside the circle.
and let 
.
- What is the domain of each function?
- If the domain of both functions is restricted to
, does f(x) become invertible? Does g(x) become invertible? - What is the domain of
?
Answers: The domain of f(x) is the interval 
, the domain for g(x) is the interval 
. Both functions will be invertible if their domain is further restricted to contain only non-negative numbers. The domain of is the interval
.
Answer: x = 2.
Find the domain of the expression and simplify the expression completely.
Answers: The domain is the interval 
.
The expression can be simplified to
