Part 1 | Test 1 | Time: 1 hour |
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- Graph the function 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 . - Determine the interval(s) where the function
- Let
*A*=(3,1),*B*=(7,-4) , and*C*=(10,9).- 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 isThe point

*C*lies outside the circle.

- Find an equation for the circle passing through the point
- Let 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 . - Solve for
*x*in the following equation:

**Answer:***x*= 2.

- Consider the algebraic expression
Find the domain of the expression and simplify the expression completely.

**Answers:**The domain is the interval . The expression can be simplified to

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