## Precalculus Practice Exam

Part 1 Test 1 Time: 1 hour

1. 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 .

2. 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 is

The point C lies outside the circle.

3. 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 .

4. Solve for x in the following equation:

5. 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

If you would like to practice another Part 1 exam, click on Next Exam.

If you would like to practice on exams for Parts 2, 3 or 4, click on Menu. It will take you back to the original menu.

Thu Jun 12 22:29:17 MDT 1997