**Question 1**

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.

ƒ(x) = 4x^{2} – 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. |

5 points

**Question 2**

Describe the right-hand and the left-hand behavior of the graph of

t(x) = 4x^{5} – 7x^{3} – 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. |

5 points

**Question 3**

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.

ƒ(x) = 3 – 5x + 3x^{2} – 5x^{3}

| 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. |

5 points

**Question 4**

Select from the following which is the polynomial function that has the given zeroes.

2,-6

| f(x) = x | |

| f(x) = x | |

| f(x) = -x | |

| f(x) = -x | |

| f(x) = x |

5 points

**Question 5**

Select from the following which is the polynomial function that has the given zeroes.

0,-2,-4

| f(x) = -x | |

| f(x) = x | |

| f(x) = x | |

| f(x) = x | |

| f(x) = x |

5 points

**Question 6**

Sketch the graph of the function by finding the zeroes of the polynomial.

f(x) = 2x^{3} – 10x^{2} + 12x

| 0,2,3 | |

| 0,2,-3 | |

| 0,-2,3 | |

| 0,2,3 | |

| 0,-2,-3 |

5 points

**Question 7**

Select the graph of the function and determine the zeroes of the polynomial.

f(x) = x^{2}(x-6)

| 0,6,-6 | |

| 0,6 | |

| 0,-6 | |

| 0,6 | |

| 0,-6 |

5 points

**Question 8**

Use the Remainder Theorem and Synthetic Division to find the function value.

g(x) = 3x^{6} + 3x^{4} – 3x^{2} + 6, g(0)

| 6 | |

| 3 | |

| -3 | |

| 8 | |

| 7 |

5 points

**Question 9**

Use the Remainder Theorem and Synthetic Division to find the function value.

f(x) = 3x^{3} – 7x + 3, f(5)

| -343 | |

| 343 | |

| 345 | |

| 340 | |

| 344 |

5 points

**Question 10**

Use the Remainder Theorem and Synthetic Division to find the function value.

h(x) = x^{3} – 4x^{2} – 9x + 7, h(4)

| -28 | |

| -27 | |

| -31 | |

| -25 | |

| -29 |

5 points

**Question 11**

Use synthetic division to divide:

(3x^{3} – 24x^{2} + 45x – 54) ÷ (x-6)

| 6x | |

| 6x | |

| 3x | |

| 3x | |

| 3x |

5 points

**Question 12**

Use synthetic division to divide:

(x^{3} – 27x + 54) ÷ (x – 3)

| x | |

| x | |

| x | |

| x | |

| x |

5 points

**Question 13**

Use synthetic division to divide:

(4x^{3} – 9x + 16x^{2} – 36) ÷ (x + 4)

| 4x | |

| 4x | |

| -4x | |

| 4x | |

| 4x |

5 points

**Question 14**

Use synthetic division to divide:

| 5x | |

| 16x | |

| 100x | |

| 20x | |

| 4x |

5 points

**Question 15**

Find all of the zeroes of the function.

(x – 3)(x + 9)^{3}

| -3,9 | |

| 3,9 | |

| -3,-9 | |

| -3,3,9 | |

| 3,-9 |

5 points

**Question 16**

Find all the rational zeroes of the function.

x^{3} – 12x^{2} + 41x – 42

| -2, -3, -7 | |

| 2, 3, 7 | |

| 2, -3, 7 | |

| -2, 3, 7 | |

| -2, 3, -7 |

5 points

**Question 17**

Determine all real zeroes of f.

f(x) = x^{3} + x^{2} – 25x – 25

| -5,1,0 | |

| 5,0,-5 | |

| -5,-1,5 | |

| -5,0,0 | |

| 5,-1,0 |

5 points

**Question 18**

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 |

5 points

**Question 19**

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 – 0.5x^{2}

What expenditure for advertising will yield a maximum profit?

| 40 | |

| 0.5 | |

| 230 | |

| 20 | |

| 115 |

5 points

**Question 20**

The total revenue R earned per day (in dollars) from a pet-sitting service is given by

R(p) = -10p^{2} + 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 |

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## A+++++ Tutorial (Reliable solution Use as a guide only)

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