Spring 2017 Final Exam Review
Topics 7-11
1. Determine the x-intercept of the function
Name: ___________________________
Date: _______________ Period: ______
.
2. For the function
. Determine the effects
the transformation has on the equation of the asymptote
of the parent function
.
3. Suppose you invest $1600 at an annual interest rate of
4.6% compounded continuously. How much will you
have in the account after 4 years?
4. Write the equation in logarithmic form.
14. Write –2x2(–5x2 + 4x3) in standard form.
15. Simplify the expression.
16. Write the polynomial in factored form. x3 + 2x2 –
15x
17. What are the zeros of the function? What are
their multiplicities?
18. What is the relative maximum and minimum of
the function?
5. Write the equation in exponential form.
19. What are the real or imaginary solutions of the
polynomial equation?
6. Write the expression as a single logarithm.
20. Divide
7. Expand the logarithmic expression.
by x + 4.
21. Use synthetic division to find P(–2) for
.
8. Solve the exponential equation.
9. Solve the logarithmic equation. Round to the
nearest ten-thousandth if necessary.
22. Use the Rational Root Theorem to list all possible
rational roots of the polynomial equation
. Do not find the actual
roots.
23. Find the roots of the polynomial equation.
10. Simplify
11. Solve
.
. Round to the nearest thousandth.
12. Classify –2x4 – x3 + 8x2 + 12 by degree.
13. Classify 8x4 + 7x3 + 5x2 + 8 by number of terms.
24. Find a third-degree polynomial equation with
rational coefficients that has roots –4 and 2 + i.
25. Find all the zeros of the equation.
26. What are the minimum and maximum values of the
function
on the interval
?
38. Write an equation for the translation of
that
has the asymptotes x = 7 and y = 6.
27. The formula for the volume of a sphere is
.
Find the radius, to the nearest hundredth, of a sphere
with a volume of 15 in.3.
39. Find any points of discontinuity for the rational
function.
40. Describe the vertical asymptote(s) and hole(s) for
28. Multiply and simplify if possible.
the graph of
29. What is the simplest form of the expression?
.
41. Simplify the rational expression. State any
restrictions on the variable.
30. What is the simplest form of the quotient?
42. What is the product in simplest form? State any
restrictions on the variable.
31. What is the simplest form of the quotient?
43. What is the quotient in simplified form? State
any restrictions on the variable.
32. What is the simplest form of the radical expression?
44. Simplify the sum.
33. Mulitiple and simplify.
45. Simplify the complex fraction.
34. How can you write the expression with rationalized
denominator?
35. Write the exponential expression
in radical form.
46. Solve the equation. Check the solution.
36. Suppose that x and y vary inversely and that
when x = 8. Write a function that models the inverse
variation and find y when x = 4.
37. Suppose that y varies jointly with w and x and inversely
with z and y = 175 when w = 5, x = 20 and z = 4. Write
the equation that models the relationship. Then find y
when w = 2, x = 24 and z = 6.
47. What are the minimum and maximum values of the
function
on the interval
?
48. What is the inverse of the function
?
49. Use composition of functions to determine whether
and
are inverses.
61. Simplify the rational expression. State any
50. What is the y-intercept of a function that is graphed by
shifting the graph of
down 8 units?
restrictions on the variable.
62. Graph the function
its domain and range.
. Determine
y
10
51. Solve
.
8
6
4
52. What is the solution of the equation?
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
53. Solve the equation. Check the solution.
–6
–8
–10
54. Solve the logarithmic equation. Round to the
nearest ten-thousandth if necessary.
Solve
.
63. What are the zeros of the function? Graph the
function.
y
10
8
55. Solve the logarithmic equation. Round to the
nearest ten-thousandth if necessary.
6
4
2
56. Simplify the expression.
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
57. Write the equation in logarithmic form.
–10
58. Write the expression as a single logarithm.
64. Simplify the sum.
59. Expand the logarithmic expression.
65. What is a cubic polynomial function in standard
form with zeros –4, –5, and 4
60. Solve the exponential equation.