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the work you submit must be substantially your own. 3) You must show your work to receive partial credit.
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copy by the due date above. 6) Please clearly indicate your answers by circling them.
1. Suppose p(x) = x2 + 8x + 6. Write the expression
p(h + 1) − 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) –6 + h
D) –6 - h
2. Find all real numbers x such that: 𝑥 4 − 53𝑥 2 + 196 = 0
3. Find a number b such that 6 is a zero of the polynomial p defined by p(x) = –36 + bx - 6x2 + x3.
A) 36
B) –36
C) 6
D) –6
4. Find a polynomial 𝑝 of degree 3 such that −3, 1 and 4 are zeros of 𝑝 and 𝑝(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 – y12 completely.
8. Write the domain of the function r(x) as a union of intervals.
5 x 7 − 6 x5 − 3
r ( x) =
x2 − 5
A)
C)
( −, − 5 ) (
( − 5, 5 )
5,
)
B)
D)
9. Find two distinct numbers x such that t ( x) =
( −, − 5 ) ( −
( −, − 5 ) ( −
)
5)(
5, 5
5,
5,
)
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 ) 4 , where f ( x) =
A) 4
B) 16
C) 0
D) -4
cx3 − 20 x 2 + 12 x − 16
.
4 x3 − 8 x 2 + x − 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 = −4 .
A) 256
B) 0.0039
C) –256
D) –0.0039
x +8
.
x − 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 − 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.
−1
19. Find a formula for the inverse function f of the indicated function f.
f ( x) = 6 x −6
−1
20. Find a formula for the inverse function f of the indicated function f.
f ( x ) = 2 9 x −5 + 3
A)
B)
21.
x + 3
log
2 + 5
f −1 ( x) =
log 9
x+3
log
2 −5
f −1 ( x) =
log 9
Find the inverse function.
A)
B)
7x − 3
10
x
7 − 10
f −1 ( x) =
3
f −1 ( x) =
C)
D)
x −3
f −1 ( x) = log
− log 9 − 5
2
x −3
log
2 +5
f −1 ( x) =
log 9
f ( x) = log7 (10 x − 3)
C)
f −1 ( x) = 10 7 x − 3
D)
f −1 ( x) =
7x + 3
10
22. Find a formula for (f 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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