Exam 1: Functions and Linear Models

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Sketch the straight line with the equation. Sketch the straight line with the equation.

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Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for   .  . Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for   .

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Sketch the straight line of the following equation. Sketch the straight line of the following equation.

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If the income If the income   is specified as a function of selling price   , which variable is independent and which one is dependent? Choose the correct letter for each question. is specified as a function of selling price If the income   is specified as a function of selling price   , which variable is independent and which one is dependent? Choose the correct letter for each question. , which variable is independent and which one is dependent? Choose the correct letter for each question.
independent variable
dependent variable
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independent variable
dependent variable
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Function Function   is   . Find   . is Function   is   . Find   . . Find Function   is   . Find   . .

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Find the equation of the given linear function. Find the equation of the given linear function.   Please enter your answer as an equation of a linear function. Please enter your answer as an equation of a linear function.

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Given Given   , find   . , find Given   , find   . .

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The position of a model train, in feet along the railroad track, is given by The position of a model train, in feet along the railroad track, is given by   after   seconds. When will the train have moved a distance of 30 feet? after The position of a model train, in feet along the railroad track, is given by   after   seconds. When will the train have moved a distance of 30 feet? seconds. When will the train have moved a distance of 30 feet?

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The table shows soybean production, in millions of tons, in Brazil's Cerrados region, as a function of the cultivated area, in millions of acres. Use technology to obtain the regression line. Round coefficients to two decimal places. The table shows soybean production, in millions of tons, in Brazil's Cerrados region, as a function of the cultivated area, in millions of acres. Use technology to obtain the regression line. Round coefficients to two decimal places.

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Calculate the slope of the straight line through the points (4, 1)and (6, -5). Try to do the calculations mentally.

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Given Given   , find   . , find Given   , find   . .

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Find the linear equation that is the straight line through (3, 5)and (9, 23). Please enter your answer as an equation in the form Find the linear equation that is the straight line through (3, 5)and (9, 23). Please enter your answer as an equation in the form   . .

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The chart shows second quarter total retail e-commerce sales in the U.S. in 1999, 2001 and 2003 ( The chart shows second quarter total retail e-commerce sales in the U.S. in 1999, 2001 and 2003 (   represents 1999). Find the regression line. Round coefficients to two decimal places. Year t 0 2 4 Sales ($ Billion)4 8 13 Use the regression line to estimate second quarter retail e-commerce sales in 2002. Round your answer to two decimal places. represents 1999). Find the regression line. Round coefficients to two decimal places. Year t 0 2 4 Sales ($ Billion)4 8 13 Use the regression line to estimate second quarter retail e-commerce sales in 2002. Round your answer to two decimal places.

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In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature   and the Celsius temperature   are related by a linear equation, find the Fahrenheit temperature that correspond to 31 C, to the nearest degree. and the Celsius temperature In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature   and the Celsius temperature   are related by a linear equation, find the Fahrenheit temperature that correspond to 31 C, to the nearest degree. are related by a linear equation, find the Fahrenheit temperature that correspond to 31 C, to the nearest degree.

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Graph shows the number of sports utility vehicles Graph shows the number of sports utility vehicles   sold in the United States.   represents sales in year   in thousands of vehicles. Find   .  sold in the United States. Graph shows the number of sports utility vehicles   sold in the United States.   represents sales in year   in thousands of vehicles. Find   .  represents sales in year Graph shows the number of sports utility vehicles   sold in the United States.   represents sales in year   in thousands of vehicles. Find   .  in thousands of vehicles. Find Graph shows the number of sports utility vehicles   sold in the United States.   represents sales in year   in thousands of vehicles. Find   .  . Graph shows the number of sports utility vehicles   sold in the United States.   represents sales in year   in thousands of vehicles. Find   .

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The following table shows the approximate average household income in the U.S. in 1995, 2002, and 2003. ( The following table shows the approximate average household income in the U.S. in 1995, 2002, and 2003. (   represents 1995.)   Which of the following kinds of models would best fit the given data? ( A , a , b , c , and m are constants.) represents 1995.) The following table shows the approximate average household income in the U.S. in 1995, 2002, and 2003. (   represents 1995.)   Which of the following kinds of models would best fit the given data? ( A , a , b , c , and m are constants.) Which of the following kinds of models would best fit the given data? ( A , a , b , c , and m are constants.)

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In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model   as a piecewise linear function of the time   in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1955. (Round you answer to the nearest integer.) as a piecewise linear function of the time In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model   as a piecewise linear function of the time   in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1955. (Round you answer to the nearest integer.) in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1955. (Round you answer to the nearest integer.)

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The value of U.S. trade with China from 1994 through 2001 can be approximated by The value of U.S. trade with China from 1994 through 2001 can be approximated by   billion dollars (   is time in years since 1994). Find an appropriate domain of   . billion dollars ( The value of U.S. trade with China from 1994 through 2001 can be approximated by   billion dollars (   is time in years since 1994). Find an appropriate domain of   . is time in years since 1994). Find an appropriate domain of The value of U.S. trade with China from 1994 through 2001 can be approximated by   billion dollars (   is time in years since 1994). Find an appropriate domain of   . .

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Match each function with the corresponding graph.
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Given Given   , find   . , find Given   , find   . .

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