Quiz 1: Chapter 1

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Quiz 1: Chapter 1 - Quiz

Reviewing concepts from Sections 1.1-1.4


Questions and Answers
  • 1. 

    Which of the following represents the domain of the function ?

    Correct Answer
    C.
  • 2. 

    Table A x 5 6 7 4 9 y -9 -5 -7 6 4 Table B x 4 7 3 15 8 y -4 -1 4 3 3 Usa Table B to find y = f(4).

    • A.

      -4

    • B.

      3

    • C.

      9

    • D.

      6

    Correct Answer
    A. -4
    Explanation
    Looking at Table B, we can see that when x = 4, y = -4. Therefore, the value of y when x = 4 is -4.

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  • 3. 

    Does  describe y as a function of x?

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The given correct answer is true because the question is asking if y is described as a function of x. If y is described as a function of x, it means that for every value of x, there is a unique value of y. This implies that there is a clear relationship between x and y, where the value of y depends on the value of x. Therefore, the statement "Does describe y as a function of x?" is true.

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  • 4. 

    Table A x 5 6 7 4 9 y 4 -5 -7 6 4 Table B x 4 7 3 15 8 y -4 -1 4 3 3 Does Table A describe x as function of y? 

    • A.

      Yes

    • B.

      No

    Correct Answer
    B. No
    Explanation
    Table A does not describe x as a function of y because for the value of y=4, there are two different corresponding values of x (5 and 9). In a function, each input (y) should have only one unique output (x), but in this case, there is a repetition of the input value y=4. Therefore, Table A does not satisfy the criteria for a function.

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  • 5. 

    One line passes through the points (-12, 16) and (-1, 38), and a second line has equation 2y + x = 23. Are the line parallel, perpendicular, or neither?

    • A.

      Parallel

    • B.

      Perpendicular

    • C.

      Neither

    Correct Answer
    B. Perpendicular
    Explanation
    The two lines are perpendicular because the product of their slopes is -1. The slope of the first line can be found using the formula (y2 - y1) / (x2 - x1), which gives (38 - 16) / (-1 - (-12)) = 22/11 = 2. The slope of the second line can be found by rearranging the equation 2y + x = 23 to y = -(1/2)x + 23/2, which has a slope of -1/2. The product of the slopes (-1/2) * 2 = -1, indicating that the lines are perpendicular.

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  • 6. 

    Which of the following represents the domain of the function ?

    Correct Answer
    B.
  • 7. 

    Write the equation that passes through (5, -3) and is parallel to the line with equation 2x + y = -3.

    Correct Answer
    y = -2x + 7
    y=-2x+7
    y = -2x+7
    y = -2x+7
    Explanation
    Don't forget that your answer should say "y = ...."

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  • 8. 

    For the function , compute the average rate of change between x = -1 and x = 2.

    Correct Answer
    3
    m = 3
    Explanation
    The average rate of change between x = -1 and x = 2 is determined by finding the difference in the function values at these two points and dividing it by the difference in the x-values. In this case, the function value is constant at 3 for all x-values, so the average rate of change is also constant and equal to 3.

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  • 9. 

    The average salary of a classroom teacher in the United States is given by f(t) = 982.06t + 32,903.77, where t is the number of years from 1990. What was the average salary in 2000?

    Correct Answer
    42724.37
    $42724.37
    $42,724.37
    f(x) = 42, 724.37
    f(x) = 42724.37
    Explanation
    The given function f(t) represents the average salary of a classroom teacher in the United States based on the number of years from 1990. To find the average salary in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the function.

    f(t) = 982.06t + 32,903.77
    f(10) = 982.06(10) + 32,903.77
    f(10) = 9,820.6 + 32,903.77
    f(10) = 42,724.37

    Therefore, the average salary in 2000 is $42,724.37.

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  • 10. 

    The equation of the line that fits the data points in the table is f(a) = 0.017924A + 0.01. Use the equation to find f(28000).

    Correct Answer
    501.882
    501.88
    f(a) = 501.882
    f(a)=501.882
    Explanation
    The given equation f(a) = 0.017924A + 0.01 represents a linear relationship between the variable a and the function f(a). To find f(28000), we substitute 28000 for A in the equation and solve for f(a). Therefore, f(28000) = 0.017924(28000) + 0.01 = 501.882.

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  • 11. 

    A company has revenue given by R(x) =564x dollars and total cost given by C(x) = 40,000 + 64x dollars, where x is the number of units poroduced and sold. Write the profit function.

    Correct Answer
    P(x) = 500x - 40000
    P(x)=500x-40000
    P(x) = 500x - 40,000
    Explanation
    Remember P(x) = R(x) - C(X). Your answer should be in simplest form.

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  • 12. 

    For the function , find .

    Correct Answer
    10
  • 13. 

    A company has determined that its profit for product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. Write the equation of the profit function P(x) for this product.

    Correct Answer
    P(x) = 4.4x - 205
    P(x)=4.4x-205
    Explanation
    Remember P(x) = R(x) - C(X). Your answer should be in simplest form.

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  • 14. 

    Whice of the following equations is the point-slope form for a linear equation?

    • A.

      Ax + by = c

    • B.

      Y = mx + b

    • C.
    • D.

      Y = b

    Correct Answer
    C.
    Explanation
    The correct answer is "y = mx + b". This equation is in the point-slope form for a linear equation, where "m" represents the slope of the line and "b" represents the y-intercept. This form allows us to easily identify the slope and y-intercept of the line by comparing the equation to the standard form, y = mx + c.

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  • 15. 

    Which of the following graphs represents the function ?

    Correct Answer
    B.

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  • Current Version
  • Mar 17, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 21, 2013
    Quiz Created by
    Tcraigsmith
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