Quiz 1: Chapter 1
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Write the equation that passes through (5, -3) and is parallel to the line with equation 2x + y = -3.
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.
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.Rate this question:
- 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.Rate this question:
- 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.Rate this question:
- 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.Rate this question:
- 6.
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.Rate this question:
- 8.
Whice of the following equations is the point-slope form for a linear equation?
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Ax + by = c
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Y = mx + b
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![Quiz 1: Chapter 1 - Quiz]()
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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.Rate this question:
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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).
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-4
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3
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9
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6
Correct Answer
A. -4Explanation
Looking at Table B, we can see that when x = 4, y = -4. Therefore, the value of y when x = 4 is -4.Rate this question:
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- 10.
Which of the following graphs represents the function ?
Correct Answer
A. -
- 11.
Does describe y as a function of x?
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True
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False
Correct Answer
A. TrueExplanation
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.Rate this question:
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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?
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Parallel
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Perpendicular
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Neither
Correct Answer
A. PerpendicularExplanation
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.Rate this question:
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- 13.
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?
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Yes
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No
Correct Answer
A. NoExplanation
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.Rate this question:
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- 15.
Which of the following represents the domain of the function ?
Correct Answer
A. -
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Current Version
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Mar 17, 2023Quiz Edited by
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Aug 21, 2013Quiz Created by
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