Download (Sections 2.3-2.8) Practice Test

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?, ?, 2011
Practice Chapter Test 3 Solutions (Sections 2.3-2.8)
1.
(4 pts.) Find the zeros for the polynomial function f(x) = x3 – 12x2 + 36x
x(x2 – 12x + 36) = 0
x(x – 6)2 = 0
Zeros = {0,6}
2. (9 pts.) The function g(x) = x4 + 4x3 – 21x2 can be factored as x2(x + 7)(x – 3) and has roots of 0,
-7, and 3. What does the graph of g(x) do at each of these zeros (circle the correct answer)?
At x = -7, the graph...
Crosses the x-axis
At x = 0, the graph...
Crosses the x-axis
At x = 3, the graph...
Crosses the x-axis
Touches the x-axis and turns around
Touches the x-axis and turns around
Touches the x-axis and turns around
3. (4 pts.) Divide using long division (6x2 – 5x – 2)  (2x – 3)
3x + 2
2x – 3 ) 6x – 5x – 2
- (6x2 – 9x)
4x – 2
- (4x – 6)
4
2
q(x) = 3x + 2 ,
r(x) = 4
4. (4 pts.) Divide (you can use synthetic division if you wish) (3x 3 + 7x2 – 3x + 8)  (x – 3)
3 | 3 7 -3 8
9 48 135
3 16 45 | 143
q(x) = 3x2 + 16x + 45
r(x) = 143
5. (4 pts.) Use the Rational Zero Theorem to list all possible rational zeros for
f(x) = x3 – 20x2 + 16x – 6
+/- 1, +/- 6, +/- 2, +/- 3
6. (4 pts.) Find the domain of the rational function h( x ) 
 6x 2
( x  5)( x  2)
{x | x ≠5,-2}
7. (4 pts.) Find the vertical asymptotes, if any, of the graph of the rational function f ( x ) 
x 3
x ( x  1)
x = 0, x = -1
8. (4 pts.) Solve the polynomial inequality (x – 5)(x + 4)
-4
-5
(-10)(-1) < 0
F
(-4 , 5)
 0 (write answer in interval notation)
5
0
-5(4) < 0
T
6
1(5) < 0
F
9. (4 pts.) Assume y varies directly as x and inversely as the square of z. If y = 46 when x = 92 and
z = 2, then find y when x = 63 and z = 3.
y = kx / z2
46 = k(92)/4
46 = k (23)
k = 2
y = 2x / z2
y = 2(63)/9
y = 14
10. (4 pts.) The number of gallons of Gatorade, G, used to dump on coach Beamer after big Hokie
victories varies directly with the amount of time the Gatorade shower should last, t. Recently, a
shower lasting 5 seconds used 5 gallons of Gatorade. How much Gatorade will be needed for a
shower lasting 60 seconds after Virginia Tech wins the ACC again?
G = kt
5 = k(5)
k = 1
G = t
G = 60
11. (X pts.) Find the roots (zeros) of f(x) = x3 + 8x2 + 11x – 20 = 0
1 | 1 8 11 -20
1 9 20
1 9 20 | 0
x2 + 9x + 20 = 0
(x + 4)(x + 5) = 0
x = {1,-4,-5}
zeros = factors of constant term / factors of leading coefficient