MA 105 WEEK 8
Question 1
Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.
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Rises to the left, falls to the right |
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Rises to the right, rises to the left |
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Falls to the left, rises to the right |
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Falls to the right |
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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) = 4×2 – 5x + 4
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Falls to the left, rises to the right |
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Falls to the left, falls to the right |
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Rises to the left, rises to the right |
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Rises to the left, falls to the right |
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Falls to the left |
Question 3
Find all the real zeroes of the polynomial function.
f(x) = x2 – 25
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-25 |
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5 |
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-5 |
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25 |
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±5 |
Question 4
Use synthetic division to divide.
(4×3 + x2 – 11x + 6) ÷ (x + 2)
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4×2 – 5x – 6 |
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4×2 – 7x + 3 |
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4×2 – 2x – 2 |
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4×2 + 5x – 12 |
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4×2 + 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 – 6×2 – 5x + 7
h(-8)
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-849 |
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-847 |
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-851 |
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-848 |
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-845 |
Question 6
Find all the rational zeroes of the function.
x3 – 12×2 + 41x – 42
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-2, -3, -7 |
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2, 3, 7 |
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2, -3, 7 |
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-2, 3, 7 |
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-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.
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$38 |
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$35 |
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$36 |
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$37 |
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$34 |
Question 8
Find the domain of the function
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Domain: all real numbers x except x = 7 |
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Domain: all real numbers x except x = ±49 |
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Domain: all real numbers x except x = ±8 |
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Domain: all real numbers x except x = -7 |
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Domain: all real numbers x except x = ±7 |
Question 9
Find the domain of the function and identify any vertical and horizontal asymptotes.
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Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 0 |
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Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asymptote: y = 0 |
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Domain: all real numbers x except x = 5 Vertical asymptote: x = 0 Horizontal asymptote: y = 2 |
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Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 2 |
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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.
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x+3; vertical asymptote: x = -3 |
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x; vertical asymptote: none |
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x; vertical asymptote: x = -3 |
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x-3; vertical asymptote: none |
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x2; vertical asymptote: none |
Question 11
Determine the equations of any horizontal and vertical asymptotes of
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horizontal: y = 5; vertical: x = 0 |
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horizontal: y = 1; vertical: x = -5 |
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horizontal: y = 1; vertical: x = 1 and x = -5 |
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horizontal: y = -1; vertical: x = -5 |
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horizontal: y = 0; vertical: none |
Question 12
Identify all intercepts of the following function.
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x-intercepts: (±3, 0) |
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no intercepts |
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x-intercepts: (-3,0) |
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x-intercepts: (0,0) |
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x-intercepts: (3,0) |
Question 13
Select the correct graph of the function.
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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.)
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1,442 deer |
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1,632 deer |
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1,594 deer |
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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
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584.191 |
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784.191 |
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-584.191 |
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684.191 |
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-784.191 |
Question 16
Select the graph of the function.
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Question 17
Use the One-to-One Property to solve the equation for x.
ex2-6 = e5x
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x = -6 |
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x = 5 |
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x = 6, -1 |
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x = -6, -1 |
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x = -6,1 |
Question 18
log366 = 1/2
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36½ = -6 |
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36½ = 6 |
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6½ = 36 |
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36½ = -1/6 |
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36½ = 1/6 |
Question 19
Write the exponential equation in logarithmic form.
272 = 729
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log27729 = 2 |
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log27729 = 1/2 |
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log72927 = 2 |
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log27729 = -2 |
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log272 = 729 |
Question 20
Find the exact value of the logarighmic expression without using a calculator.
4 ln e7
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7 |
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28 |
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4 |
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e |
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1 |
Question 21
Condense the expression to the logarithm of a single quantity.
ln310 + ln3x
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ln3(10 – x) |
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ln310/x |
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ln3(10 + x) |
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ln310x |
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ln310x |
Question 22
Solve for x.
6x = 1,296
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6 |
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10 |
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4 |
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-6 |
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-4 |
Question 23
Solve the exponential equation algebraically. Approximate the result to three decimal places.
ex – 8 = 12
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ln20 ≈ 2.485 |
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ln20 ≈ 2.996 |
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ln20 ≈ -2.485 |
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ln20 ≈ 2.079 |
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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?
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1 year |
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14.40 years |
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13.86 years |
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14.86 years |
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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.
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2,418,774 |
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2,419,774 |
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2,421,774 |
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2,420,774 |
