Math 8

QUESTION 1

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

		Rises to the left, falls to the right
		Rises to the right, rises to the left
		Falls to the left, rises to the right
		Falls to the right
		Falls to the left, falls to the right

4 points   

QUESTION 2

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

f(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

4 points   

QUESTION 3

1. Find all the real zeroes of the polynomial function.

f(x) = x2 - 25

		-25
		5
		-5
		25
		±5

4 points   

QUESTION 4

1. Use synthetic division to divide.

(4x3 + x2 - 11x + 6) ÷ (x + 2)

		4x2 - 5x - 6
		4x2 - 7x + 3
		4x2 - 2x - 2
		4x2 + 5x - 12
		4x2 + 7x - 4

4 points   

QUESTION 5

1. Use the Remainder Theorem and synthetic division to find the function value.  Verify your answers using another method.

h(x) = x3 - 6x2 - 5x + 7

h(-8)

		-849
		-847
		-851
		-848
		-845

4 points   

QUESTION 6

1. 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

4 points   

QUESTION 7

1. The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by 

R(p) = -25p2 + 1700p

where p is the price per unit (in dollars).

Find the unit price that will yield a maximum revenue.

		$38
		$35
		$36
		$37
		$34

4 points   

QUESTION 8

1. Find the domain of the function 

		Domain: all real numbers x except x = 7
		Domain: all real numbers x except x = ±49
		Domain: all real numbers x except x = ±8
		Domain: all real numbers x except x = -7
		Domain: all real numbers x except x = ±7

4 points   

QUESTION 9

1. Find the domain of the function and identify any vertical and horizontal asymptotes.

		Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 0
		Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asymptote: y = 0
		Domain: all real numbers x except x = 5 Vertical asymptote: x = 0 Horizontal asymptote: y = 2
		Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 2
		Domain: all real numbers x except x = 5 Vertical asymptote: x = 5 Horizontal asymptote: y = 0

4 points   

QUESTION 10

1. Simplify f and find any vertical asymptotes of f.

		x+3; vertical asymptote: x = -3
		x; vertical asymptote: none
		x; vertical asymptote: x = -3
		x-3; vertical asymptote: none
		x2; vertical asymptote: none

4 points   

QUESTION 11

1. Determine the equations of any horizontal and vertical asymptotes of

		horizontal: y = 5; vertical: x = 0
		horizontal: y = 1; vertical: x = -5
		horizontal: y = 1; vertical: x = 1 and x = -5
		horizontal: y = -1; vertical: x = -5
		horizontal: y = 0; vertical: none

4 points   

QUESTION 12

1. Identify all intercepts of the following function.

		x-intercepts: (±3, 0)
		no intercepts
		x-intercepts: (-3,0)
		x-intercepts: (0,0)
		x-intercepts: (3,0)

4 points   

QUESTION 13

1. Select the correct graph of the function.

4 points   

QUESTION 14

1. The game commission introduces 100 deer into newly acquired state game lands.  The population N of the herd is modeled by

where t is the time in years.  Find the populations when t=40.  (Round your answer to the nearest whole number.)

		1,442 deer
		1,632 deer
		1,594 deer
		1,550 deer
		1,500 deer

4 points   

QUESTION 15

1. Evaluate the function at the indicated value of x.  Round your result to three decimal places.

Function: f(x) = 6000(6x)    Value: x = -1.3

		584.191
		784.191
		-584.191
		684.191
		-784.191

4 points   

QUESTION 16

1. Select the graph of the function.

4 points   

QUESTION 17

1. Use the One-to-One Property to solve the equation for x.

ex2-6 = e5x

		x = -6
		x = 5
		x = 6, -1
		x = -6, -1
		x = -6,1

4 points   

QUESTION 18

1. log366 = 1/2

		36½ = -6
		36½ = 6
		6½ = 36
		36½ = -1/6
		36½ = 1/6

4 points   

QUESTION 19

1. Write the exponential equation in logarithmic form.

272 = 729

		log27729 = 2
		log27729 = 1/2
		log72927 = 2
		log27729 = -2
		log272 = 729

4 points   

QUESTION 20

1. Find the exact value of the logarighmic expression without using a calculator.

4 ln e7

		7
		28
		4
		e
		1

4 points   

QUESTION 21

1. Condense the expression to the logarithm of a single quantity.

ln310 + ln3x

		ln3(10 - x)
		ln310/x
		ln3(10 + x)
		ln310x
		ln310x

4 points   

QUESTION 22

1. Solve for x.

6x = 1,296

		6
		10
		4
		-6
		-4

4 points   

QUESTION 23

1. Solve the exponential equation algebraically.  Approximate the result to three decimal places.

ex - 8 = 12

		ln20 ≈ 2.485
		ln20 ≈ 2.996
		ln20 ≈ -2.485
		ln20 ≈ 2.079
		ln20 ≈ -2.996

4 points   

QUESTION 24

1. An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously.  How long will it take to double the investment?

		1 year
		14.40 years
		13.86 years
		14.86 years
		13.40 years

4 points   

QUESTION 25

1. The populations (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modele by   where t represents the year, with t = 0 corresponding to 2000.  Use the model to find the numbers of cell sites in the year 2001.

		2,418,774
		2,419,774
		2,421,774
		2,420,774
		2,422,774