Precalculus I--Part 4--Test 7--With Answers.

Precalculus Practice Exam

Part 4 Test 7 Time: 2 hours

- Express the angle in radians.
  Answer: 9.546148 radians.
- Express 546.954 radians in format.
  Answer:
For the function , determine the:
- (h) amplitude,
  Answer: 6.
- (i) period,
  Answer:
- vertical shift,
  
  Answer: 10 up.
- phase shift,
  Answer: to the right.
- domain,
  Answer: all real numbers.
- range.
  Answer
- Can f(t)=-2? Explain.
  Answer: no because the range of f(t) goes is between 4 and 16, and since -2 is not in between those numbers, therefore f(t) can't never be -2.
Simplify each expression:
- .
  Answer:
- .
  Answer:
- Answer:
Given that and , find the remaining five trigonometric functions of the angle .

Answer:
Find if . Restrict domain if necessary.
Answer: . The restricted domain is .
Find the inverse of the following function (restrict the domain if necessary):
- Restrict the domain to all .
  Answer:
- Answer: The domain is restricted to all x > 10 .
If you invested $1,000 for 4 years as follows:
- Years 1 and 2 compounded weekly at 11%, and years 3 and 4 continuously at 13%.
- What simple interest rate would give you the same balance as the above after four years?
  Answer: At the end of 2 years we will have approximately $1245.79, and at the end of 4 years we will have approximately $1615.69.
  
  A simple interest rate of 12.74 % pear year will yield the same balance as the above after four years.
Find a polynomial function that passes through the point (3,24), has a double zero of 3 and zeros 1 and -1
- Of degree 3.
  
  Answer: This is not possible. If 3 is a double zero, then we have 4 zeros above. The smallest degree of a polynomial having 1, -1 and double 3 as their zeros has to be 4 according to the fundamental theorem of algebra.
- Of degree 4.
  Answer: (x-3)(x-3)(x+1)(x-1) or
- Of degree 6.
  Answer:
  
  There are many possible solutions for this. However all the exponents of each of the terms must add up to 6.
Solve for x:

Answer: The domain is restricted to all x>1. By solving this equation algebraically we get two solutions, x=1 and x=6, but since x=1 is not in the domain of the original equation, then the only solution is x=6.
Find the quadratic function whose graph contains the points (1,-2),(2,1) and (-1,10).
Answer: The equation is .
Suppose you are given a polynomial function of degree four with a relative maximum of 10 located at x=0, a relative maximum of 22 located at x=10, and a relative maximum of -5 located at x=4. On what interval(s) is the function:
- Increasing?
  Answer: The function is increasing on the intervals .
- Decreasing?
  Answer: The function is decreasing on the intervals .
- Give two intervals where at least one of the zeros of the polynomial exists.
  Answer: Two intervals are and .
  There are several other solutions.

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Fri, March 6, 1998