Reference no: EM13926961

QUESTION 1:

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

f(x) = 1/5 x³ + 5x

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

QUESTION 2:

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

QUESTION 3:

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

f(x) = x² - 25

-25

5

-5

25

±5

QUESTION 4:

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

QUESTION 5:

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

QUESTION 6:

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

QUESTION 7:

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

QUESTION 8:

Find the domain of the function

f(x) = 8x²/x²-49

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

QUESTION 9:

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

f(x) = 2/(x-5)³

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

QUESTION 10:

Simplify f and find any vertical asymptotes of f.

f(x) = x²(x+3)/x² + 3x

x+3; vertical asymptote: x = -3

x; vertical asymptote: none

x; vertical asymptote: x = -3

x-3; vertical asymptote: none

x2; vertical asymptote: none

QUESTION 11:

Determine the equations of any horizontal and vertical asymptotes of

f(x) = x²-1/(x² + 4x -5)

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

QUESTION 12:

Identify all intercepts of the following function.

g(x) = (x² + 3)/x

x-intercepts: (±3, 0)

no intercepts

x-intercepts: (-3,0)

x-intercepts: (0,0)

x-intercepts: (3,0)

QUESTION 13:

Select the correct graph of the function.

f(x) = 8/(x-5)

QUESTION 14:

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

N = 30(5+3t)/1 +0.04t, t ≥ 0

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

QUESTION 15:

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

QUESTION 16:

Select the graph of the function.

f(x) = (1/3)^-x

QUESTION 17:

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

ex^2-6 = e^5x

x = -6

x = 5

x = 6, -1

x = -6, -1

x = -6,1

QUESTION 18:

log₃₆6 = 1/2

36½ = -6

36½ = 6

6½ = 36

36½ = -1/6

36½ = 1/6

QUESTION 19:

Write the exponential equation in logarithmic form.

27² = 729

log27729 = 2

log27729 = 1/2

log72927 = 2

log27729 = -2

log272 = 729

QUESTION 20:

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

4 ln e⁷

7

28

4

e

QUESTION 21:

Condense the expression to the logarithm of a single quantity.

ln₃10 + ln₃x

ln3(10 - x)

ln310/x

ln3(10 + x)

ln310x

ln310x

QUESTION 22:

Solve for x.

6x = 1,296

6

10

4

-6

-4

QUESTION 23:

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

QUESTION 24:

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

QUESTION 25:

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