1.Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.
ƒ(x) = 4x2 - 5x + 4
Falls to the left, rises to the right.
Falls to the left, falls to the right.
Rises to the left, rises to the right.
Rises to the left, falls to the right.
Falls to the left.
2. Describe the right-hand and the left-hand behavior of the graph of
t(x) = 4x5 - 7x3 - 13
Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
3. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.
ƒ(x) = 3 - 5x + 3x2 - 5x3
Falls to the left, rises to the right.
Falls to the left, falls to the right.
Rises to the left, rises to the right.
Rises to the left, falls to the right.
Falls to the left.
4. Select from the following which is the polynomial function that has the given zeroes.
2,-6
f(x) = x2 - 4x + 12
f(x) = x2 + 4x + 12
f(x) = -x2 -4x - 12
f(x) = -x2 + 4x - 12
f(x) = x2 + 4x - 12
5. Select from the following which is the polynomial function that has the given zeroes.
0,-2,-4
f(x) = -x3 + 6x2 + 8x
f(x) = x3 - 6x2 + 8x
f(x) = x3 + 6x2 + 8x
f(x) = x3 - 6x2 - 8x
f(x) = x3 + 6x2 - 8x
6. Use the Remainder Theorem and Synthetic Division to find the function value. g(x) = 3x6 + 3x4 - 3x2 + 6, g(0)
6
3
-3
8
7
7. Use the Remainder Theorem and Synthetic Division to find the function value.
f(x) = 3x3 - 7x + 3, f(5)
-343
343
345
340
344
8. Use the Remainder Theorem and Synthetic Division to find the function value.
h(x) = x3 - 4x2 - 9x + 7, h(4)
-28
-27
-31
-25
-29
9. Use synthetic division to divide: (3x3 - 24x2 + 45x - 54) ÷ (x-6)
6x2 - 3x - 9, x ≠ 6
6x2 -3x - 9, x ≠ 6
3x2 - 6x + 9, x ≠ 6
3x2 - 6x - 9, x ≠ 6
3x2 + 6x + 9, x ≠ 6
10. Use synthetic division to divide: (x3 - 27x + 54) ÷ (x - 3)
x2 + 3x - 18, x ≠ 3
x2 - 3x - 27, x ≠ 3
x2 + 9x + 18, x ≠ 3
x2 + 9x - 6, x ≠ 3
x2 + 6x + 9, x ≠ 3
11. Use synthetic division to divide: (4x3 - 9x + 16x2 - 36) ÷ (x + 4)
4x2 - 9, x ≠ -4
4x2 + 9, x ≠ -4
-4x2 - 9, x ≠ -4
4x3 - 9, x ≠ -4
4x3 + 9, x ≠ -4
12. Use synthetic division to divide:
5x2 + 45x + 25, x ≠ 1/5
16x2 + 80x + 20, x ≠ 1/5
100x2 + 45x + 400, x ≠ 1/5
20x2 + 180x + 400, x ≠ 1/5
4x2 + 21x + 20, x ≠ 1/5
13. Find all of the zeroes of the function.
(x - 3)(x + 9)3
-3,9
3,9
-3,-9
-3,3,9
3,-9
14. Find all the rational zeroes of the function.
x3 - 12x2 + 41x - 42
-2, -3, -7
2, 3, 7
2, -3, 7
-2, 3, 7
-2, 3, -7
15. Determine all real zeroes of f.
f(x) = x3 + x2 - 25x - 25
-5,1,0
5,0,-5
-5,-1,5
-5,0,0
5,-1,0
16. The height, h(x), of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?
28 feet
13 feet
18 feet
23 feet
16 feet
17. The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model.
P(x) = 230 + 40x - 0.5x2
What expenditure for advertising will yield a maximum profit?
40
0.5
230
20
115
18. The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) = -10p2 + 130p, where p is the price charged per pet (in dollars).
Find the price that will yield a maximum revenue.
$7.5
$6.5
$8.5
$9.5
$10.5