the polynomial function, algebra homework help

the polynomial function, algebra homework help

QUESTION 1

00001.

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

00002.

ƒ(x) = 4x² – 5x + 4

00003.

		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.

00004.

5 points

QUESTION 2

00001.

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

00002.

t(x) = 4x⁵ – 7x³ – 13

00003.

		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.

00004.

5 points

QUESTION 3

00001.

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

00002.

ƒ(x) = 3 – 5x + 3x² – 5x³

00003.

		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.

00004.

5 points

QUESTION 4

00001.

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

00002.

2,-6

00003.

		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

00004.

5 points

QUESTION 5

00001.

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

00002.

0,-2,-4

00003.

		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

00004.

5 points

QUESTION 6

00001.

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

00002.

f(x) = 2x³ – 10x² + 12x

00003.

		0,2,3
		0,2,-3
		0,-2,3
		0,2,3
		0,-2,-3

00004.

5 points

QUESTION 7

00001.

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

00002.

f(x) = x²(x-6)

00003.

		0,6,-6
		0,6
		0,-6
		0,6
		0,-6

00004.

5 points

QUESTION 8

00001.

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

00002.

g(x) = 3x⁶ + 3x⁴ – 3x² + 6, g(0)

00003.

		6
		3
		-3
		8
		7

00004.

5 points

QUESTION 9

00001.

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

00002.

f(x) = 3x³ – 7x + 3, f(5)

00003.

		-343
		343
		345
		340
		344

00004.

5 points

QUESTION 10

00001.

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

00002.

h(x) = x³ – 4x² – 9x + 7, h(4)

00003.

		-28
		-27
		-31
		-25
		-29

00004.

5 points

QUESTION 11

00001.

Use synthetic division to divide:

00002.

(3x³ – 24x² + 45x – 54) ÷ (x-6)

00003.

		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

00004.

5 points

QUESTION 12

00001.

Use synthetic division to divide:

00002.

(x³ – 27x + 54) ÷ (x – 3)

00003.

		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

00004.

5 points

QUESTION 13

00001.

Use synthetic division to divide:

00002.

(4x³ – 9x + 16x² – 36) ÷ (x + 4)

00003.

		4x2 – 9, x ≠ -4
		4x2 + 9, x ≠ -4
		-4x2 – 9, x ≠ -4
		4x3 – 9, x ≠ -4
		4x3 + 9, x ≠ -4

00004.

5 points

QUESTION 14

00001.

Use synthetic division to divide:

00002.

00003.

		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

00004.

5 points

QUESTION 15

00001.

Find all of the zeroes of the function.

00002.

(x – 3)(x + 9)³

00003.

		-3,9
		3,9
		-3,-9
		-3,3,9
		3,-9

00004.

5 points

QUESTION 16

00001.

Find all the rational zeroes of the function.

00002.

x³ – 12x² + 41x – 42

00003.

		-2, -3, -7
		2, 3, 7
		2, -3, 7
		-2, 3, 7
		-2, 3, -7

00004.

5 points

QUESTION 17

00001.

Determine all real zeroes of f.

00002.

f(x) = x³ + x² – 25x – 25

00003.

		-5,1,0
		5,0,-5
		-5,-1,5
		-5,0,0
		5,-1,0

00004.

5 points

QUESTION 18

00001.

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?

00002.

		28 feet
		13 feet
		18 feet
		23 feet
		16 feet

00003.

5 points

QUESTION 19

00001.

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.

00002.

P(x) = 230 + 40x – 0.5x²

00003.

What expenditure for advertising will yield a maximum profit?

00004.

		40
		0.5
		230
		20
		115

00005.

5 points

QUESTION 20

00001.

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

00002.

R(p) = -10p² + 130p

00003.

where p is the price charged per pet (in dollars).

00004.

Find the price that will yield a maximum revenue.

00005.

		$7.5
		$6.5
		$8.5
		$9.5
		$10.5

00006.

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