Final Exam Practice Solutions

1) Suppose is a function with zeros 2 (multiplicity 2), (multiplicity 3), and 1 (multiplicity 1). The function is a degree 6 polynomial whose graph contains the point Find (in factored form).

2) Find the complex zeros of Possible zeros: 72

72

Answer:

2) Find the complex zeros of Possible zeros:

Answer:

3) Find all asymptotes of each function.

 

4) Solve.

5) Solve.

6) If and , find and the domain of .

7) Find the inverse of the following function. What is the domain of the inverse? The range?

8) Solve:

9) Solve:Please give an exact answer and an approximation.

10) How long will it take an investment to quadruple in value if the interest rate is 8%, compounded annually?

11) Find the vertex, focus, and directrix of each parabola. Which direction does it open?a)

b)

12) Write the equation of each hyperbola.a) Vertices ; Focus

b) Vertex Center Focus

13) Solve.

14) Find the quadratic function that passes through the points

Place the coefficients and constants in a matrix and find the reduced row echelon form (or use determinants or use inverses)

15) The sum of two numbers is 9 and the difference of their squares is 27. Find the two numbers.

6 and 3

16) Find the sum.

17) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 11th term is and the term is .

17) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 11th term is and the term is .OR

18) Bella is setting up a cereal display at her grocery store. The bottom row contains 48 cereal boxes and each successive row has two less cereal boxes. How many total cereal boxes does she need to make a display with 23 rows?

19) Determine whether each series converges or diverges. If it converges, find its sum.a)

b)

20) Use the binomial theorem to answer each question. You may use your calculator to compute the combinations.a) What is the coefficient of in The two exponents must add up to 9.

b) What is the second tem of The second term has an exponent on the constant term of one less than the term. Since the term is the second, it’s an exponent of 1.OR The exponent on the variable counts down →5, 4. The exponent on the variable is 4.In either case, the term is: