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

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