Midterm Review
1. What is the domain and range for the parent function for x 2  1 and for the translated function?
________________(Parent Function)
__________________________(Translated Function)
2. What are the coordinates of the transformed point? (3, 4); vertical shift 3 units up and horizontal shift 2
units right_______________________________
3. What numbers complete the table of the transformed function?
Reflection across y-axis
X
y
8
2
1
1
0
0
1
1
8
2
4. Use a table to perform a vertical stretch of y  f(x) by a factor of 2. Graph using the same coordinate plane
as the original function.
x
y
5.The graph of a function passes through the points (9, 6) and (12, 3). What are the coordinates of these
points after the function has been compressed vertically by a factor of
1
?__________ ____________
3
6. Graph the data from the table. Describe the parent function and the transformation that best approximates
the data set.
x
4
2
0
1
3
y
21
9
5
6
14
________________________________________
7. Graph the relationship from time to number of organisms living in a petri
dish during the course of an experiment. Use the parent function that best approximates the data to predict
the number of organisms living in the dish
at hour 6.
Organisms in Petri Dish
Time (h)
0
1
2
3
4
No. of
Organisms
4
8
11
12
16
8.What is the parent function for  x  3  1 _______________________________
9. Let g(x) be a vertical translation up 2 units followed by a reflection over the y-axis of f(x)  3x  4. Write the
rule for g(x)._______________________________
10. Let g(x) be a horizontal compression by a factor of
1
3
of f  x   x  2 . Write the rule for g(x). _________
3
4
11. What describes the transformation in terms of f(x)? Horizontal shift left 6 units _____________________
12. What describes the transformation in terms of f(x)? Vertical stretch of 12 _________________________
13. What transformation describes the equation from its parent equation? f  x  3  11 ____________________
14. What transformation describes the equation from its parent equation?
3
f  x  _______________________
4
15. Make a scatter plot of the data in the table below, identify the correlation, and then sketch a line of best fit and find its
equation.
x
12
15
25
19
y
11
17
23
19
________________________________________
16. What is the type of correlation shown?
17. What is the type of correlation shown?
20. Using f(x)  x2, describe the transformation
2
1

that yields f (x )   x  3   10 .
4


21. Use this description to write a quadratic
equation in vertex form: A vertical stretch by a
factor of 5, a translation 7 units to the left, and
a translation 1 unit up.
18. What is the approximate correlation
coefficient?
19. What is the approximate correlation
coefficient?
22. Consider h(x)  3x2  9x  4. Identify its vertex
and y-intercept.
23. State whether there is a minimum or
maximum of g(x)  2x2  5x  3 and identify
it.
24. Find all zeros of the trinomial
k(x)  2x2  x  55.
30. Solve 81x2  8  0.
31. Solve 3x2  6x  4  0.
25. Solve 64x2  1.
32. For the discriminant
26. Write a trinomial h(x) with zeros of x  4 and
x  17.
 2
2
 4  1  1 , identify
the number of solutions and their type(s).
33. Solve 2x2  17x  4  5.
27. Identify the vertex of g(x)  (x  15)2 9.
28. Write the quadratic equation in vertex form.
c(x)  x2  10x  4
34. Solve 3x2  x  10  -8.
29. Simplify i 9 108 .
35. Fay threw a basketball from the basketball court toward the hoop. The quadratic equation that models
the path of the ball is p(t)  16t2  20t  6. If the hoop is 10 feet high, how long is the ball in the air
before the ball goes through the hoop?
Simplify.
36.
2  i5
i3
 1

37.  5  4i  
i
10


38. Write a 9th degree monomial with x, y, and z
as variables.
45. What is the complete factorization of
(16x3  54)?
39. Write a 5th degree trinomial with a leading
coefficient of 4.
40. What is (2x2  6x  1) subtracted from
(2x3  3x  2)?


46. If 5 and 5  5 are two of the roots of a
third degree polynomial with integer
coefficients, what is the other root?
47. What are all the roots of 12x5  30x4  72x3?
41. Find (x2  2)(2x2  5x  3).
48. Write a simplified third degree polynomial with
2 and 3 as its only zeros.
42. What is (c  2)5?
49. What are all the roots of x3  2  2x2  x?
43. Find (x3  18x  8) divided by (x  4).
44. If (x  a) is a factor of (x4  5x3  21x2  23x 
8), what number could be a?
50. What is the degree of the simplest polynomial
with integer coefficients that has 3 , 3, 3i,
and 3  3i as zeros?
51. If the behavior of the function is down on the
left and down on the right, what do you know
about the degree and the coefficients of P(x)?
52. Draw a graph of an odd function with exactly four real zeros and a positive leading coefficient.
53. If f(x)  x3  2x2  3x  1, find g(x)  f(x  2).
54. If f(x)  x4  x3  x2  2x  3, find g(x), the
reflection of f(x) across the y-axis followed by
a reflection across the x-axis.
55. What is the degree of the polynomial that best
fits the data below?.
56. How many turning points does a quartic
polynomial function having 4 distinct real roots
have?
x
1
2
3
4
5
6
7
y
15
3
1
3
9
5
87
57. If f (x)  (r)x is an example of exponential
decay, what must be true of r?
58. Write an exponential growth model.
61. The population of Greenfield was 52,500 at
the beginning of 1980. Its population steadily
decreased by 2.5% per year from 1980
through 1990. Write an expression for
Greenfield’s population at the end of 1990.
59. Write an exponential decay model.
60. An oil painting from the early twentieth
century, originally purchased for $8500, has
been increasing in value by 7.5% for the 24
years since its purchase. Write an expression
that gives its current value.
()
62. What is the inverse of f x =
3
x +1?
4
63. The table below gives the coordinates of a function. Write the coordinates for it’s inverse function.
x
y
-2
0
-1
2
0
5
1
9
64. What is the logarithmic form of 63  216?
68. Simplify log109  10log 5.
69. Simplify log3 25  log3 4.
65. What is the exponential form of logx 4 = 3?
3
70. Write in logarithmic form of 814  27 .
66. Evaluate log9 27  log27 9.
71. Evaluate log0.5 4  log4 0.5.
67. Express 2log 3  3log 2  log 6 as a single
logarithm.
72. Express 3log5 4  5log5 2 as a single
logarithm.
5-3x
= 810
73. 2