Expert: Sherman D. - 10/20/2008

Question
1) If f(x) = 2x^2 - x - 3 and g(x) = x + 1, find f + g
    I think it is b. It has to be either...
a) 2x^2 - 2
b) 2x^2 - 4x
c) x^3 - 2x + 3
d) x^3 - x^2 + 2x


2) If f(x) = 3x - 4 and g (x) = x + 2, find f + g
   I think it is a. It has to be either...
a) x + 4
b) 4x - 2
c) 2x - 4
d) 4x


3) If f (x) = 3x - 4 and g (x) = x + 2 find f*g (f times g)
    I think it is b. It has to be either...
a) 3x^2 + 2x
b) 2x - 8
c) x + 2
d) 3x^2 + 2 - 8


4) If f (x) = 3x and g(x) = x - 5, find (f*g)(x)
    I think it is d. It has to be either...
a) 2x + 5
b) 3x - 15
c) 5x - 3
d) 3x - 5


5) If f(x) = 5x + 2 and g(x) = 3x - 4, find (f*g)(x)
     I think it is c. It has to be either...
a) 18x - 5
b) x + 18
c) 3x + 8
d) 15x - 18


6) Find the distance between points (5, 1) and (8, 5)
   I think it is c. It has to be either...
a) 23
b) 20
c) 13
d) 5


7) Find the distance between two points (0,0 and (3, 5)
   I think it is a. It has to be either...
a) The square root of 34
b) The square root of 54
c) The square root of 17
d) The square root of 85



8) Find the midpoint of the line between the two points (10, 4) and (2, 6)
   I think it is c. It has to be either...
a) (6, 5)
b) (5, 3)
c) (2, 1)
d) (5, 5)


9) Find the midpoint of the line between the two points (-2, -1) and (-8, 6)
   I think it is d. It has to be either...
a) (1/3, 3)
b) (2, 8)
c) (1, 1/5)
d) (-5, 5/2)


10) Write the standard form of the equation of a circle with the center (0, 0) r = 8
       I think it is a. It has to be either...
a) x^2 + y^2 = 64
b) x^2 + y^2 = 16
c) x^2 + y^2 = 8
d) x^2 + y^2 = 4



11) Write the standard form of the equation of a circle with the center (-3, 5) r = 3
     I think it is c. It has to be either...
a) (x + 2^2) + (y + 3^2) = 18
b) x^2 + y^2 = 19
c) (x + 3)^2 (y - 5^2) = 9
d) (x + 5^2) + (y - 3^2) = 9


12) Write the standard form of the equation of a circle with center (-2, 0) r = 6
      I think it is a. It has to be either...
a) x^2 + y^2 = 36
b) (x + 2^2) + y^2 = 36
c) x^2 + (y - 2^2) = 6
d) x^2 + y^2 = 6


13) If f(x) = 3x - 4 and g(x) = x + 2, find f - g
    I think it is d. It has to be either...
a) 2x + 2
b) 2x - 6
c) x + 2
d) x - 6

Answer
1.)
f(x) = 2x^2 - x - 3
g(x) = x + 1

f + g = (2x^2 - x - 3) + (x + 1)
f + g = 2x^2 - x - 3 + x + 1
f + g = 2x^2 - 2

ANS : A.

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2.)
f(x) = 3x - 4
g(x) = x + 2

f + g = 3x - 4 + x + 2
f + g = 4x - 2

ANS : B.

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3.)
f(x) = 3x - 4
g(x) = x + 2

f * g = (3x - 4)(x + 2) = 3x^2 + 6x - 4x - 8 = 3x^2 + 2x - 8
ANS :
Rewrite it and the answer is D.

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4.)
f(x) = 3x
g(x) = x - 5

f(x - 5) = 3(x - 5) = 3x - 15
ANS : B.)

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5.)
f(x) = 5x + 2
g(x) = 3x - 4

f(3x - 4) = 5(3x - 4) + 2
f(3x - 4) = 15x - 20 + 2
f(3x - 4) = 15x - 18
ANS : D.

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6.)
(5,1) and (8,5)
D = sqrt((8 - 5)^2 + (5 - 1)^2)
D = sqrt(3^2 + 4^2)
D = sqrt(9 + 16)
D = sqrt(25)
D = 5
ANS : D.

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7.)
D = sqrt((x2 - x1)^2 - (y2 - y1)^2)

(0,0) and (3,5)
D = sqrt((0 - 3)^2 + (5 - 0)^2)
D = sqrt(3^2 + 5^2)
D = sqrt(9 + 25)
D = sqrt(34)
ANS : A.

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8.)
(10,4) and (2,6)
m = (2 + 10)/2 , (6 + 4)/2
m = (12/2),(10/2)
m = (6,5)
ANS : A.

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9.)
(-2,-1) and (-8,6)
m = (-8 + (-2))/2 , (6 + (-1))/2
m = (-10/2), (5/2)
m = (-5,(5/2))
ANS : D.

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10.)
(x - 0)^2 + (y - 0)^2 = 8^2
x^2 + y^2 = 64
ANS : A.

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11.)
(x - (-3))^2 + (y - 5)^2 = 3^2
(x + 3)^2 + (y - 5)^2 = 9
ANS :
If you rewire it, the answer is C.

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12.)
in (x - h)^2 + (y - k)^2 = r^2, (h,k) is the center
(x - (-2))^2 + (y - 0)^2 = 6^2
(x + 2)^2 + y^2 = 36

ANS :
If you rewrite it, then the answer is B.)

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13.)
f(x) = 3x - 4
g(x) = x + 2

f - g = (3x - 4) - (x + 2) = 3x - 4 - x - 2 = 2x - 6
ANS : B.

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