Quiz 1: Chapter 1

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  • 1/15 Questions

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

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Quiz 1: Chapter 1 - Quiz
About This Quiz

Quiz 1: Chapter 1 assesses understanding of mathematical functions, including domain identification, function evaluation, and analysis of graphical representations. It tests skills in interpreting data tables and determining relationships between variables, crucial for learners in enhancing mathematical reasoning.

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

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

    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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  • 3. 

    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?

    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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  • 4. 

    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).

    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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  • 5. 

    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.

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

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  • 6. 
    For the function , find . - ProProfs

    For the function , find .

  • 7. 

    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.

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

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  • 8. 

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

    • Ax + by = c

    • Y = mx + b

    • Quiz 1: Chapter 1 - Quiz

    • Y = b

    Correct Answer
    A.
    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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  • 9. 

    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).

    • -4

    • 3

    • 9

    • 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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  • 10. 
    Which of the following graphs represents the function ? - ProProfs

    Which of the following graphs represents the function ?

    Correct Answer
    A.
  • 11. 
    Does  describe y as a function of x? - ProProfs

    Does  describe y as a function of x?

    • True

    • 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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  • 12. 

    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?

    • Parallel

    • Perpendicular

    • Neither

    Correct Answer
    A. 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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  • 13. 
    Which of the following represents the domain of the function ? - ProProfs

    Which of the following represents the domain of the function ?

    Correct Answer
    A.
  • 14. 

    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? 

    • Yes

    • No

    Correct Answer
    A. 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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  • 15. 
    Which of the following represents the domain of the function ? - ProProfs

    Which of the following represents the domain of the function ?

    Correct Answer
    A.

Quiz Review Timeline (Updated): Mar 17, 2023 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

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