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1. Suppose p(x) = x2 + 8x + 6. Write the expression
p(h + 1) β p(1)
as a sum of terms, each of which is a
h
constant times a power of h.
A) 10 - h
B) 10 + h
C) β6 + h
D) β6 - h
2. Find all real numbers x such that: π₯ 4 β 53π₯ 2 + 196 = 0
3. Find a number b such that 6 is a zero of the polynomial p defined by p(x) = β36 + bx - 6x2 + x3.
A) 36
B) β36
C) 6
D) β6
4. Find a polynomial π of degree 3 such that β3, 1 and 4 are zeros of π and π(0) = 4 .
5. If p(x) = a2x2 + 4x + 5 and q(x) = (1 - 2a)x2 - 8x - 5, find a real number a such that (p + q)(x) has
degree 1.
A) 4
B) -4
C) 0
D) 1
6. Find all choices of (b, c, d) such that 4 and 1 are the only zeros of the polynomial p(x) = x3 + bx2 + cx +
d.
7. Factor x24 β y12 completely.
8. Write the domain of the function r(x) as a union of intervals.
5 x 7 β 6 x5 β 3
r ( x) =
x2 β 5
A)
C)
( βο₯, β 5 ) ο (
( β 5, 5 )
5, ο₯
)
B)
D)
9. Find two distinct numbers x such that t ( x) =
( βο₯, β 5 ) ο ( β
( βο₯, β 5 ) ο ( β
)
5)ο(
5, 5
5,
5, ο₯
)
1
x + 17
, where t ( x) = 2
.
2
x + 16
x2
R( x)
in the form G ( x) +
, where q is the denominator of the given
x+9
q( x)
expression and G and R are polynomials with deg R < deg q.
10. Write the expression
11. Find a constant c such that f (10100 ) ο» 4 , where f ( x) =
A) 4
B) 16
C) 0
D) -4
cx3 β 20 x 2 + 12 x β 16
.
4 x3 β 8 x 2 + x β 3
12. Find the asymptotes of the graph of the function r ( x) =
13. Evaluate the indicated expression. log25 56
A) 6
14.
B) 0.33
C) 3
D) 12
Evaluate the indicated expression. log 7
A) 3/2
B) -3/2
C) 2/3
1
343
D) -2/3
15. Find a number t such that log 4 t = β4 .
A) 256
B) 0.0039
C) β256
D) β0.0039
x +8
.
x β 17 x + 72
2
16. Find a number x such that log5 (8 x + 3) = 3 . Round your answer to two decimal places.
17. Find a number t such that
10t β 1
= 0.2 . Round your answer to four decimal places.
10t + 1
18. Find a number x such that 102x + 10x = 30. Round your answer to four decimal places.
β1
19. Find a formula for the inverse function f of the indicated function f.
f ( x) = 6 x β6
β1
20. Find a formula for the inverse function f of the indicated function f.
f ( x ) = 2 ο 9 x β5 + 3
A)
B)
21.
ο¦ x + 3οΆ
log ο§
ο·
ο¨ 2 οΈ + 5
f β1 ( x) =
log 9
ο¦ x+3οΆ
log ο§
ο·
ο¨ 2 οΈ β5
f β1 ( x) =
log 9
Find the inverse function.
A)
B)
7x β 3
10
x
7 β 10
f β1 ( x) =
3
f β1 ( x) =
C)
D)
ο¦ x β3οΆ
f β1 ( x) = log ο§
ο· β log 9 β 5
ο¨ 2 οΈ
ο¦ x β3οΆ
log ο§
ο·
ο¨ 2 οΈ +5
f β1 ( x) =
log 9
f ( x) = log7 (10 x β 3)
C)
f β1 ( x) = 10 ο 7 x β 3
D)
f β1 ( x) =
7x + 3
10
22. Find a formula for (f ο― g)(x) assuming that f ( x) = 41+7 x and g ( x) = log 4 x .
23. Find all such numbers x such that log_2(3x + 4) = 4 holds.

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Anonymous

I was having a hard time with this subject, and this was a great help.