196
Chapters P–6
Final Exam
Test Form A
Name __________________ Date ____________
FINAL EXAM
Chapters P–6
Class __________________ Section __________
1. Solve for x:
4
3
#
$ 7.
x
x!1
(a) #1, 5
(d)
(b) 3
#7 ± #77
14
(c)
#3 ± #37
7
(e) None of these
1
2. Find the domain of
#x2
# 7x # 8
.
(a) %#1, 8$
(b) !# %, #1$ ! %8, %"
(d) !#1, 8"
(e) None of these
(c) !# %, #1" ! !8, %"
3. Find the distance between the origin and the midpoint of the two points !3, 3" and !3, 5".
(a) 3#2
(b) 7
(c) #34
(d) 5
(e) None of these
4. Determine the standard equation of the circle with radius 2 and center !#1, 3".
(a) !x # 1" 2 ! ! y # 3" 2 $ 2
(b) !x # 1" 2 ! ! y # 3" 2 $ 4
(c) !x ! 1" 2 ! ! y # 3" 2 $ 2
(d) !x ! 1" 2 ! ! y # 3" 2 $ 4
(e) None of these
(a) 2x ! 3y $ 8
(b) 2x # 3y $ 12
(d) 3x # 2y $ #8
(e) None of these
6. Given f !x" $ 2 # 3x2, find
(a) 2
(d)
6x2 ! 6x"x ! 9!"x" 2
"x
(c) 2x ! 3y $ #12
f !x ! "x" # f !x"
.
"x
(b) #6x # 3"x
(e) None of these
(c) 2x ! "x
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5. Find the equation of the line that is perpendicular to 2x ! 3y $ 12 but has the
same y-intercept.
Chapters P–6
7. Write the height h of the rectangle as a function of x.
y
y = x +1
(a) h!x" $ x2 # 5x ! 3
4
(b) h!x" $ #x2 ! 5x # 3
3
(c) h!x" $ 3 # 5x ! x2
(d) h!x" $ 5x # 3 !
2
x2
1
y = x 2 - 4x + 4
t
(e) None of these
8. Given f !x" $
Final Exam
1
2
3
4
5
1
and g!x" $ x ! 3, find the domain of ! f ' g"!x".
x2 # 1
(a) !# %, %"
(b) !# %, #1", !#1, 1", !1, %"
(c) !# %, #4", !#4, #2", !#2, %"
(d) %#3, %"
(e) None of these
9. Determine whether the function f !x" $
(a) Not one-to-one
(d) f #1!x" $ #
7
x!2
7
is one-to-one. If it is, find its inverse.
x!2
(b) f #1!x" $
x!2
7
(c) f #1!x" $
7 # 2x
x
(e) None of these
10. Divide: !9x3 # 6x2 # 8x # 3" & !3x ! 2".
8
7&3
(a) 3x2 # x #
3
3x ! 2
(c) 3x2 # 4x #
(b) 3x2 # 4x # 2 !
3
3x ! 2
(d) 3x2 # 4x #
7
3x ! 2
16
23&3
!
3
3x ! 2
© Houghton Mifflin Company. All rights reserved.
(e) None of these
11. Perform the indicated operation and write the result in standard form:
(a) #
2
16
# i
13 13
(b)
(d) #
2
16
! i
13 13
(e) None of these
2 ! 4i
.
3 # 2i
2
16
# i
13 13
(c)
2
16
! i
13 13
12. Write the polynomial in completely factored form: f !x" $ x3 # x ! 6.
(a) !x ! 2"!x2 # 2x ! 3"
(b) !x ! 2"!x # 1 ! #2i"!x ! 1 # #2i"
(c) !x ! 2"!x # 1 # #2i"!x # 1 ! #2i"
(d) !x ! 2"!x ! 1 # #2i"!x ! 1 ! #2i"
(e) None of these
197
198
Chapters P–6
Final Exam
13. Find the limit: lim
x→#9
x2 ! 6x # 27
.
x!9
(a) #12
(b) The limit does not exist.
(d) 0
(e) None of these
14. Find the limit: lim
#x ! 4 # 2
x
x→0
.
1
4
(a) 0
(b)
(d) 1
(e) None of these
15. Find the limit: lim!
x→4
(c)
(b) !%
(d) 4
(e) None of these
(c) # %
16. Find an equation of the tangent line to the graph of f !x" $
(a) x ! y ! 3 $ 0
(b) x # y $ 1
(d) x ! y $ 6
(e) None of these
(a)
%
x2 # x
.
!x # 4"2
(a) 0
17. Find f(!x": f !x" $
(c) #3
1
at the point !2, 1".
x#1
(c) y # 1 $ #
!x # 2"
!x # 1"2
x2 # 4x
.
#x
3x3&2 # 4
2x1&2
(b)
(d) x 3&2 # 4x1&2
2x # 4
#x
(c)
2x # 4
1&! 2#x"
(e) None of these
(a) The velocity at time t $ 1 is 27.
(b) The velocity is a constant.
(c) The initial position is 51.
(d) The initial velocity is #24.
(e) None of these
19. Find the derivative: y $
(a)
12
!3x # 1"2
(d) #
12
!3x # 1"2
4
.
3x # 1
(b) 0
(e) None of these
(c)
4
3
© Houghton Mifflin Company. All rights reserved.
18. The position function for a particular object is s $ #12t2 ! 51t ! 38. Which statement is true?

Testing – Device Problem Analysis Dr. Lynn Fuller

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