15. The graph shows a transformation of f ( x ) = x 2 . f open x close equals , x squared , .  What is an equation of the graph?

    

    1. g ( x ) = ( x − 2 ) 2 − 3 g open x close equals . open x minus 2 close squared . minus 3
    2. g ( x ) = ( x − 2 ) 2 + 3 g open x close equals . open x minus 2 close squared . plus 3
    3. g ( x ) = ( x + 2 ) 2 − 3 g open x close equals . open x plus 2 close squared . minus 3
    4. g ( x ) = ( x + 2 ) 2 + 3 g open x close equals . open x plus 2 close squared . plus 3

16. The total cost of x + 2 markers is x 3 + 5 x 2 + 2 x − 8 . x cubed , plus 5 , x squared , plus 2 x minus 8 .

    What is the cost of each marker?

    6. x 2 + 3 x − 4 x squared , plus 3 x minus 4
    7. x 2 − 3 x + 4 x squared , minus 3 x plus 4
    8. x 2 − 3 x − 4 x squared , minus 3 x minus 4
    9. x 2 + 5 x + 2 x squared , plus 5 x plus 2

GRIDDED RESPONSE

17. Let g ( x ) = x − 3 g open x close equals x minus 3  and h ( x ) = x 2 + 6 . h open x close equals , x squared , plus 6 .  What is ( h ∘ g ) ( 1 ) ? open h composition g close open 1 close question mark
18. A laptop comes without any programs installed on it. Each program costs $20 and the laptop you want costs $319. What is the greatest number of programs you can buy if you want to spend at most $500 for the laptop?
19. You are building an entertainment center with shelves that are x in. deep by x in. long. The height of the unit will be twice the depth. If the volume of the unit will be 8 , 192  in  3 , 8 comma 192 , in cubed . comma what is the height, in inches, of the entertainment center?
20. Use Descartes' Rule of Signs to find the maximum number of positive real roots of P ( x ) = 5 x 4 + x 3 − 4 x 2 + 3 x + 1 = 0 . p open x close equals , 5 x to the fourth , plus , x cubed , minus 4 x 2 plus 3 x plus 1 equals 0 .
21. Using the discriminant, determine the number of real roots of the equation 2 x 2 + 3 x = 4 . 2 x squared , plus 3 x equals 4 .
22. What is the quotient 8 x 6 y 12 3 4 x 4 y 8 ? fraction cube root of 8 , x to the sixth , y to the twelfth end root , , over square root of 4 , x to the fourth , y to the eighth end root end fraction . question mark
23. What is the solution of 4 + 3 x + 5 = 7 ? 4 plus . square root of 3 x plus 5 end root . equals 7 . question mark
24. Simplify the expression 256 − 3 4 . 256 super negative , 3 fourths end super . .
25. All 385 tickets for a high-school play sold in 10 days. The ticket receipts totaled $1960. If the cost of a child's ticket was $4 and the cost of an adult's ticket was $6, how many adult tickets were sold?
26. What is the x-value of the x-intercept of the graph of f ( x ) = x 2 + 4 x + 4 ? f open x close equals , x squared , plus 4 x plus 4 question mark

Short Response

27. You are given that f ( x ) = x 2 + 4  and  g ( x ) = 3 x − 1 . f open x close equals , x squared , plus 4 , and , g open x close equals 3 x minus 1 .
    1. What are the domain and range of f(x) and g(x)?
    2. Find f(x) + g(x).
    3. What is the domain of your answer to part (b)?
28. Two friends went shopping together. One friend bought 2 hats and 1 shirt and spent $70, while the other friend bought 1 hat and 3 shirts and spent $85. Use a graph to determine the costs of each shirt and hat.
29. A student found that a cubic function has zeros 16 and 1 − 2 i 1 minus 2 i  with a leading coefficient of 3. What is the constant term of this polynomial function with real coefficients?
30. Describe the graph of the polynomial function f ( x ) = − x 6 + 3 x 5 + 4 x − 10 . f open x close equals negative , x to the sixth , plus , 3 x to the fifth , plus 4 x minus 10 .  What is its end behavior?

Decide whether the following statements are always, sometimes, or never true.

31. If n is a real number, then 0 n = 0 . 0 to the n , equals 0 .
32. If a and b are rational numbers, then the product of ( a + b ) open , eh plus square root of b , close  and its conjugate is a rational number.

Extended Response

33. An online music store is having a promotion. Customers receive a $5 rebate if they buy any regular priced CD at $13 each. They can also receive 15% off if they register as a store member.
    1. What functions model the two discounts?
    2. In which order should the discounts be applied for the customer to receive the greatest discount?
    3. Use your answer from part (b) to determine the amount a customer will save if she buys 5 CDs.

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