1.    The product of 2 and 98 can be determined by viewing the problem as 2 × (100 – 2) and using which   

        of the following number properties?

A.     distributive

         B.      associative

C.     commutative

         D.     transitive

  

2.      A building contractor has n days to complete a house project. If he uses one-third of the time to repair the roof and five days to paint the house, how many days will he have left to complete the project?

A.      ⅓n + 5

B.      ⅓n – 5

B.      ⅔n + 5

D.      ⅔n – 5

   

3.    The equation  x = ⅞y + 18  can be solved for y to yield which of the following?

A.     y = 8/7x – 18

B.      y = ⅞x + 18

C.      y = 8/7(x – 18)

D.     y = ⅞(18 – x)

 4. True or False. The two functions f and g defined by 

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive
                                   are equal?
5. If functions f and g have domains Df and Dg respectively, then the domain of f / g is given by 

(A) the union of Df and Dg 

(B) the intersection of Df and Dg 

(C) the intersection of Df and Dg without the zeros of function g 

(D) None of the above
6. True or False. The graph of f(x) and that of f(x + 2) are the same 


7. Let the closed interval [a , b] be the domain of function f. The domain of f(x - 3) is given by

(A) the open interval (a , b)

(B) the closed interval [a , b]

(C) the closed interval [a - 3 , b - 3]

(D) the closed interval [a + 3 , b + 3]


8. Let the interval (a , +infinity) be the range of function f. The range of f(x) - 4 is given by

(A) the interval (a - 4 , +infinity)

(B) the interval (a + 4, +infinity)

(C) the interval (a, +infinity)

(C) None of the above

9. True or False. The equation y = | x | , with y >= 0, represents y as a function of x.

10. True or False. The equation x = | y | , with x >= 0, represents y as a function of x.

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Answer:

4. False. Two functions are equal if their rules are equal and their domains are the same. 

5. (C). Division by zero is not allowed in mathematics. Students tend to forget this point. 

6. False. The graph of f(x + 2) is that of f(x) shifted 2 units to the left.

7. (D). The graph of f(x - 3) is that of f(x) shifted 3 units to the right. To shift the closed interval [a , b] to the   right you need to add 3 units to the endpoints a and b of the interval.

8. (A). If the range of f is given by the interval (a , +infinity), we can write the following inequality

f(x) > a

add - 4 to both sides on the inequality to obtain

f(x) - 4 > a - 4

The last inequality suggests that the range of f(x) - 4 is (a - 4, +infinity)

9. True.

10. False. Solve for y to find that y = | x | or y = -| x |; for one value of the independent variable x we have two values of the dependent variable y.