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Skip navigation linksMATH105. COLLEGE ALGEBRA (MATH105-2) > TAKE ASSESSMENT: EXAM 3

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 Question 1

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State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

f(x) = 9x3 + 8x2 - 6

    

Question 1 answers

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No; the last term has no variable

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Yes; degree 5

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Yes; degree 3

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Yes; degree 6

    

 

Question 2 text  Question 2

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Use the graph to determine the domain and range of the function.




    

Question 2 answers

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domain: {x|x ≠ -4, x ≠ 4}
range: {y|y ≤ 0 or y > 1}

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domain: {x|x ≠ -4, x ≠ 4}
range: {y|y ≤ 0 or y ≥ 1}

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domain: {x|x ≤ 0 or x > 1}
range: {y|y ≠ -4, y ≠ 4}

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domain: all real numbers
range: all real numbers

    

 

Question 3 text  Question 3

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Solve the equation in the real number system.

x3 + 9x2 + 26x + 24 = 0

    

Question 3 answers

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{-4, -2, -3}

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{2, 4}

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{3, 2, 4}

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{-4, -2}

    

 

Question 4 text  Question 4

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Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) =

    

Question 4 answers

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(5, 0)

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(2, 0)

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(-2, 0), (2, 0)

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(- 8, 0)

    

 

Question 5 text  Question 5

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Solve the inequality.

x4< 36x2

    

Question 5 answers

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(-∞, -6) or (0, 6)

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(-∞, -6) or (6, ∞)

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(-6, 0) or (6, ∞)

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(-6, 0) or (0, 6)

    

 

Question 6 text  Question 6

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Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

f(x) = (x - 5)3

    

Question 6 answers

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above the x-axis: (-∞, 5)
below the x-axis: (5, ∞)

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above the x-axis: (-∞, 5), (5, ∞)
below the x-axis: no intervals

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above the x-axis: no intervals
below the x-axis: (-∞, 5), (5, ∞)

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above the x-axis: (5, ∞)
below the x-axis: (-∞, 5)

    

 

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*          Question 7

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Find the power function that the graph of f resembles for large values of |x|.

f(x) = (x + 5)2

    

Question 7 answers

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y = x10

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y = x25

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y = x2

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y = x5

    

 

Question 8 text  Question 8

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Determine where the function is increasing and where it is decreasing.

f(x) = -x2 - 4x + 5

    

Question 8 answers

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increasing on (-∞, 9)
decreasing on (9, ∞)

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increasing on (-2, ∞)
decreasing on (-∞, -2)

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increasing on (-∞, -2)
decreasing on (-2, ∞)

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increasing on (9, ∞)
decreasing on (-∞, 9)

    

 

Question 9 text  Question 9

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Solve.

While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 162 newtons when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 50 kilograms, find the force a passenger experiences when the car is moving at 40 kilometers per hour and the passenger has a mass of 100 kilograms.

    

Question 9 answers

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128 newtons

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144 newtons

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160 newtons

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176 newtons

    

 

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*        Question 10

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Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.

f(x) = 3x4 - 6x3 + 4x2 - 2x + 1

    

Question 10 answers

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no real roots; f(x) = (x2 + 1)(3x2 + 1)

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1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)

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-1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)

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-1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)

    

 

Question 11 text  Question 11

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Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.

f(x) =

    

Question 11 answers

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symmetry with respect to the y-axis

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symmetry with respect to the origin

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neither

    

 

Question 12 text  Question 12

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For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept.

f(x) = x4(x2 - 3)

    

Question 12 answers

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0, multiplicity 4, touches x-axis;
, multiplicity 1, crosses x-axis;
-, multiplicity 1, crosses x-axis

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0, multiplicity 4, touches x-axis

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0, multiplicity 4, crosses x-axis;
, multiplicity 1, touches x-axis;
-, multiplicity 1, touches x-axis

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0, multiplicity 4, crosses x-axis

    

 

Question 13 text  Question 13

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Solve the inequality.

≥ 0

    

Question 13 answers

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(-∞, -7) or [-2, 6) or [12, ∞)

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(-∞, -7) or [12, ∞)

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(-7, -2] or (6, 12]

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(-∞, -7) or [-2, 0) or (0, 6) or [12, ∞)

    

 

Question 14 text  Question 14

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Find the domain of the rational function.

f(x) =

    

Question 14 answers

     

 

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Question 15 text  Question 15

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Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = -2x4 + 2x2 + 4; [-2, -1]

    

Question 15 answers

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f(-2) = 20 and f(-1) = 5; no

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f(-2) = -20 and f(-1) = 4; yes

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f(-2) = 20 and f(-1) = -4; yes

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f(-2) = -20 and f(-1) = -4; no

    

 

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*         Question 16

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State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

4(x - 1)12(x + 1)9

    

Question 16 answers

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Yes; degree 48

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Yes; degree 21

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Yes; degree 4

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Yes; degree 12

    

 

Question 17 text  Question 17

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Determine the domain and the range of the function.

f(x) = x2 + 10x

    

Question 17 answers

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domain: all real numbers
range: {y|y ≥ -25}

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domain: {x|x ≥ 5}
range: {y|y ≥ 25}

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domain: {x|x ≥ -5}
range: {y|y ≥ -25}

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domain: all real numbers
range: {y|y ≥ 25}

    

 

Question 18 text  Question 18

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Use the given zero to find the remaining zeros of the function.

f(x) = x3 + 2x2 + 5x - 26; zero: -2 + 3i

    

Question 18 answers

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3 - 2i, -2

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3 - 2i, 2

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-2 - 3i, -2

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-2 - 3i, 2

    

 

Question 19 text  Question 19

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Solve the problem.

A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Which function below describes the total cost of the material as a function of the radius r of the cylinder?

    

Question 19 answers

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C(r) = 0.08πr2 +

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C(r) = 0.16πr2 +

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C(r) = 0.16πr2 +

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C(r) = 0.08πr2 +

    

 

Question 20 text  Question 20

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Find the rational zeros of the polynomial. List any irrational zeros correct to two decimal places.

f(x) = x4 - x3 - 7x2 + 5x + 10

    

Question 20 answers

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rational zeros: 2, -1; irrational zeros ≈ 2.24, -2.24

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rational zeros: -2, 1; irrational zeros ≈ -2.47, 2.47

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rational zeros: -2, 1; irrational zeros ≈ 2.24, -2.24

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rational zeros: 2, -1; irrational zeros ≈ -2.47, 2.47

    

 

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