# MA 105 WEEK 8

Question 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 |

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

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

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.

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.

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

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.

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.

Question 14

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 |

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.

Question 17

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 |

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 | ||

1 |

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 population in the year 2001.

2,418,774 | ||

2,419,774 | ||

2,421,774 | ||

2,420,774 |

*No answers yet*