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Study Guide For Honors Pre-calculus Final
Date: December 16,2013
Chapters 1-6 except 5.4


Read Chapter Summaries at the end of each chapter. Study the chapter tests.
Solve the following review problems:
1. State the domain of the following function in interval notation: f ( x) 
[A]  7,  
[B]  7, 
[C]  , 
5
x7
[D]  ,  7   7, 
2. Which of the following must be true?
I.
If f(x) = x3/4 – 1 and f(k) = 63, then k = 64.
II.
If ( 8x)(1/2)x-1 = 163x, then x = 1/10.
III.
If 5x+5x+5x+5x+5x = 525, then x = 5.
IV.
A)
B)
C)
D)
E)
If f(x) =
, then g(x) = f-1(x) =
.
I and II
II and IV
III and IV
I, II, and IV
II, III and IV
3. Solve the quadratic inequality for x:
[A]  ,  3 or 5, 
[B]  3, 5
x 2  2 x  15  0
[C]  ,  3 or 5,  
 ,
 4 or 2, 5
[C]
 ,
 4 or  2, 5
2
[D]  ,  4 or  2, 5
5. State the domain of the following function:
3

, 
4

[A] 
 3, 5
x5
0
x  2x  8
[B]  4, 2 or 5,  
4. Solve the rational inequality for x:
[A]
[D]
3

[B]  ,  
4

y  3x  4
4

, 
3

[C] 
4

[D]  ,  
3

6. If f ( x)   f ( x) for every value of x in the domain of the function f , then which one of the following is
true about f ?
[A] f is called an odd function and its graph is symmetric about the y-axis.
[B] f is called an even function and its graph is symmetric about the y-axis.
[C] f is called an odd function and its graph is symmetric about the origin.
[D] f is called an even function and its graph is symmetric about the origin.
7. The graph of y  3 x  5 can be obtained by doing which of the following transformations of the graph
of y  x ?
[A] reflect about the x-axis, stretch by a factor of 3, shift up 5 units.
[B] shift down 5 units, reflect about the y-axis, stretch by a factor of 3.
[C] reflect about the x-axis, stretch by a factor of 3, shift down 5 units.
[D] reflect about the x-axis, shrink by a factor of 3, shift down 5 units.
 f 
  5 
g
8. If f ( x)  x 2  9 and g ( x)  x  3 , then 
[B] x  3
[A] 5( x  3)
9. If f ( x)  2 x  4 and g ( x)  3x  1 , then
[A] x  3
[C]
1
8
[D] 8
 f  g  ( x) 
[C]  x  3
[B] 5 x 2  3x
[D] 5x  3
10. If f ( x)  x 2  1 and g ( x)  x  2 , then ( f  g )( x) 
[A] x 2  4 x  5
[B] x 2  3
[C] x 2  1
11. If f ( x)  7 x  3 and g ( x)  x 2  4 , what is ( f  g )( 2) ?
[A]  53
[B] 59
[C] 125
12. If f ( x) 
[A]
4
3x  8
3
x  2 , then f 1 ( x) 
4
4
8
[B] x 
3
3
[C]
4
8
x
3
3
[D] x 2  2 x  5
[D] 292
[D]
4
x2
3
13. Which one of the following is true about the graph of a one-to-one function of x ?
[A] It is symmetric about the y-axis.
[B] It is symmetric about the x-axis.
[C] It will pass through the ordered pair (1, 1).
[D] It will pass the horizontal line test.
14. Which one of the following equations have the given roots, 3 and  4i ?
[A] x 3  3x 2  16 x  48
[B] x 3  3x 2  16 x  48
[C] x 3  3x 2  16 x  48
[D] x 3  3x 2  16 x  48
15. Write the following as a product of linear factors given that 1 and 3 are zeros:
f ( x)  x 4  2 x3  x 2  8x  12
[A] ( x  1)( x  3)( x  2i )( x  2i )
[B] ( x  1)( x  3)( x  2i )( x  2i )
[C] ( x  1)( x  3)( x  2i )( x  2i )
[D] ( x  2)( x  2)( x  3)( x  1)
x2  4
x2
[B]  , 2 or  2,  
16. State the domain of the following function in interval notation: f ( x) 
[A]
 , 2 or  2, 
[C]  , 
9
7
[B] y  0
[A] x 
1
, x5
2
[B] x 
1
, x  5
2
4
7
2
[D] y  0
5x 2  4
x3
 4 
[C] 
,0
 3 


[B]  0,
4 

3 
f ( x) 
[B] (5, 0)
[D] (3, 0)
5 x
x5
[C] (1, 0)
21. If P varies inversely as w, and P 
[A] 1
[D] y 
f ( x) 
20. Find the x  intercept:
[A] (0, 1)
1
4
4x  9
2x  9x  5
9
[C] x 
4
f ( x) 
19. Find the y  intercept:
[A] (0, 3)
x
[C]
18. Find the vertical asymptote(s):
 2 or  2, 2 or  2,  
4x 1
7x  9
f ( x) 
17. Find the horizontal asymptote:
[A] y 
 ,
[D]
[B] 16
[D] (–1, 0)
2
1
1
when w  , then what is P when w  ?
3
4
6
4
[C]
[D] 4
9
22. If y varies directly as u and varies inversely as the square of v, and y  7 when u  9 and v  6 , then find
the constant of variation.
[A]
7 6
9
[B]
7
4
[C]
28
9
[D] 28
23. The number of spiders, S (t ) , remaining within a 10-foot radius of their birthplace t days after birth is given


by the formula: S (t )  200 20.2t . Find the number of spiders present within this radius 10 days after
their birth.
[A] 0
[B] 5
[C] 50
[D] 800
A)
B)
C)
D)
E)
24. What are the zeros of the equation 4x-1-20x-2-24x-3 = 0?
0, 6,-1
0,2, -3
0, -6,1
6,-1
-1,6
8 2
1
[C] log3 (2)  8 [D] log 8    2
3
3
25. Write the equation in its equivalent logarithmic form:
[A] log 2 (8)  3
[B] log 8 (2) 
1
3
 1 

 729 
26. Evaluate the expression: log 9 
[A]  3
[B] 3
27. What is the domain for f ( x)  log 2 ( x  1) ?
[A] 0, 
[D]  81
[C] 81
[B]  1,  
[C]
 1, 
[B]
log b (8)
 log b (8)  log b (3)
log b (3)
[D] (, )
28. Which one of the following is true?
[A] e ln(x )  x for any real number x.
[C]
log b (8) 8

log b (3) 3
[D] log 2 (7) 
29. Write as a single logarithm whose coefficient is 1:
[A] logb (13)
log( 7)
log( 2)
2logb (8)  logb (3)
 64 

 3
[C] log b 
[B] logb (61)
 
30. Expand the logarithmic expression: ln 3e 2
[A] 2 ln(3)  ln(e)
[B] (2 ln 3)  1
[C] 2  ln(3)
[D] logb (10)
[D] 2  ln(3)
31. If 5 x  29 , then x equals
[A]
ln(29)
ln(5)
[B]
ln(5)
ln(29)
 29 

 5 
[C] ln 
5
2
[D] ln  
32. Solve for x: log 7 (3x  9)  log 7 (2 x  6)  0
[A] 3
[B] all real numbers
[C]  3
[D] No solution
33. Solve for x. If there are two solutions, state their sum. If there is one solution, state that answer.
log( x  9)  log( x )  1
[A]  9
[B] 9
[C]  1
[D] 1
34. If $2500 is invested in the account that pays interest compounded continuously at a rate of 4%, how long
will it take to double the investment? Hint: A  Pe rt
[A] 2.8 years
[B] 13.0 years
[C] 14.2 years
[D] 17.3 years
35. The spread of a flu virus through a particular population is modeled by y 
1000
where y is the total
1  990e0.7 t
number of people infected after t days. In how many days will 530 people be infected with the virus?
(Round your answer to the nearest whole number.)
[A] 8 days
[B] 9 days
[C] 10 days
[D] 11 days
36. Which of the following functions has a zero, vertical asymptote and a horizontal asymptote?
A)
B)
C)
37. Describe the transformation from f(x) to g(x): f(x) = ex and g(x) = e5x- 5
f(x) is:
A) Compressed horizontally by a factor of 5 and shifted down by 5 units.
B) Stretched horizontally by a factor of 1/5 and shifted down by 5 units.
C) Compressed horizontally by a factor of 1/5 and shifted right by 5 units.
D) Stretched horizontally by a factor of 1/5 and left by 5 units.
E) Compressed horizontally by a factor of 1/5 and shifted down by 5 units.
D)
38.
Which of the following is false about f(x) shown above?
A) It is an even function.
B) It s degree is 3.
C) It has 2 absolute minima and 1 relative maximum.
D) It is decreasing for all real numbers o x less than -1 and between 0 and 1.
39.
Which of the following can be the equation of the graph above?
A) (x+2)(x-2)²
B) (x-2)³
C) (x+2)²(x-2)
D) (x-2)²(x+2)²