12. Which expression represents the solution to 4 x = 13 ? 4 to the x , equals 13 question mark
    6. log   13 log 4 fraction log 13 , over log 4 end fraction
    7. log 4 + log 13 log base 4 , plus , log base 13
    8. log   4 log 13 fraction log 4 , over log , 13 end fraction
    9. log 13 4 log base 13 , 4
13. If f ( x ) = x 2 f open x close equals , x squared  and g ( x ) = x − 1 , g open x close equals x minus 1 comma  which statement is true?
    1. ( f ∘ g ) ( x ) ≥ ( g ∘ f ) ( x ) open f composition g close open x close greater than or equal to open g composition f close open x close  for all values of x.
    2. ( f ∘ g ) ( x ) ≤ ( g ∘ f ) ( x ) open f composition g close open x close less than or equal to open g composition f close open x close  for all values of x.
    3. ( f ∘ g ) ( x ) = ( g ∘ f ) ( x ) open f composition g close open x close equals open g composition f close open x close  only for x = 1. x equals 1.
    4. ( f ∘ g ) ( x ) ≠ ( g ∘ f ) ( x ) open f composition g close open x close not equal to open g composition f close open x close  for any value of x.
14. If g ( x ) = x 2 − 4 g open x close equals , x squared , minus 4  and h ( x ) = 4 x − 6 , h open x close equals 4 x minus 6 comma  which expression is equal to ( g h ) ( x ) ? open , g over h , close . open x close , question mark
    6. 4 x − 6 x 2 − 4 fraction 4 x minus 6 , over x squared , minus 4 end fraction
    7. x 2 − 2 4 x − 3 fraction x squared , minus 2 , over 4 x minus 3 end fraction
    8. x 2 − 4 − ( 4 x − 6 ) x squared , minus 4 minus open 4 x minus 6 close
    9. ( x + 2 ) ( x − 2 ) 2 ( 2 x − 3 ) fraction open , x plus 2 , close . open , x minus 2 , close , over 2 . open , 2 x minus 3 , close end fraction

GRIDDED RESPONSE

15. Suppose that x and y vary inversely. What is the constant of variation if x = 12 x equals 12  when y = 4 ? y equals 4 question mark
16. Solve for x : 5 2 x − 2 = 15 x 2 − 1 . x colon . fraction 5 , over 2 x minus 2 end fraction . equals . fraction 15 , over x squared , minus 1 end fraction . .
17. Solve for x : log ( x − 3 ) = 3 . x colon log open x minus 3 close equals 3 .

18. What is the value of the x-coordinate of the solution of the system of equations?

    { 2 x + y = 6 y − 3 = x left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus y equals 6 , row2 column 1 , y minus 3 equals x , end table

19. What is the remainder when x 4 − 3 x 2 + 7 x + 3 x to the fourth , minus , 3 x squared , plus 7 x plus 3  is divided by x − 2 ? x minus 2 question mark
20. The product of three consecutive even integers is − 2688 . negative , 2688 , .  What is the value of the largest integer?
21. What is the smallest zero of f ( x ) = 2 x 5 − 4 x 2 + 3 x + 7 ? f open x close equals , 2 x to the fifth , minus , 4 x squared , plus 3 x plus 7 question mark  Round your answer to the nearest hundredth.
22. What number do you add to each side of the equation when you solve x 2 + 5 x = 4 x squared , plus 5 x equals 4  by completing the square?
23. How many real roots does y = x 2 − 3 x + 7 y equals , x squared , minus 3 x plus 7  have?

Short Response

24. Sketch the graph of y = x − 2 ( x − 2 ) ( x − 1 ) . y equals . fraction x minus 2 , over open , x minus 2 , close . open , x minus 1 , close end fraction . .
25. Solve the inequality | 2 x − 5 | < 9 . vertical line 2 x minus 5 vertical line less than 9 .  Graph the solution.
26. Solve 2 x 2 − 11 = 12 x . 2 x squared , minus 11 equals , 12 to the x , .
27. Solve the equation 2 g 2 d − c = 3 x fraction 2 , g squared , over d end fraction . minus c equals 3 x  for g. Show your work.
28. Factor x 3 − 12 x 2 + 35 x x cubed , minus , 12 x squared , plus 35 x  completely.
29. Explain how you know that the graph of f ( x ) = − x 4 − 3 x + 7 f open x close equals negative , x to the fourth , minus 3 x plus 7  does not have up and down end behavior.
30. Graph y = 3 x + 2 − 5 . y equals . 3 super x plus 2 end super . minus 5 .

Extended Response

31. Explain how to find an equation for the translation of y = 3 x y equals , 3 over x  that has asymptotes at x = − 13 x equals negative 13  and y = 5. y equals 5.
32. What is the inverse of y = x 2 + 15 ? y equals , x squared , plus 15 question mark  Is the inverse a function? Explain.
33. A third−degree polynomial equation with rational coefficients has roots − 4 negative 4  and − 4 i . negative 4 i .  If the leading coefficient of the equation is 3 2 , 3 halves , comma  what is the equation? Show your work.
34. Graph y + 2 < | x − 4 | . y plus 2 less than vertical line x minus 4 vertical line .  How did you decide where to shade and whether the boundary was a dashed or a solid line?

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