different linear functions are represented below.Function 1Function 210-yy-2-5- 1-10-8-2-2-6-4610110-415-6-8--10-Function 3Function 4y=-4x-1The slope is 3 and they-intercept is -4.nswer the following questions.(a) Which function's graph is the least steep?Continue 23:11 1y=-4x-1The slope is 3 and they-intercept is -4.er the following questions.a) Which function's graph is the least steep?O Function 1 O Function 2 O Function 3 O Function 4(b) Which function has the graph with the greatest y-intercept?O Function 1 O Function 2 O Function 3 O Function 4(c) Which functions have graphs with slopes less than -3?(Check all that apply.)O Function 1 O Function 2 O Function 3 O Function 4ContinueSend a chat

Answered: Function 1 Function 2 10fy y -2 - 5 6-…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.1: Linear Functions

Problem 1TI: If f(x) is a linear function, and (2,3) and (0,4) are points on the line, find the slope. Is this...

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When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12
Later High School Graduates This is a continuation of Exercise 16. The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.
If f(x) is a linear function, and (2,3) and (0,4) are points on the line, find the slope. Is this functionincreasing ordecreasing?
When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of changes is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change is the same over each interval. This shows the data are linear, even though the differences in y are not constant. Then find a linear model for the data. x 1 2 5 6 y 7 10 19 22

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Function 1 Function 2 10fy y -2 - 5 6- -1 2. -10 -8 -6- -4 -2 6 10 1 10 4- 2 15 -6 -8- -10- Function 3 Function 4 y=-4x-1 The slope is 3 and the y-intercept is -4. er the following questions. a) Which function's graph is the least steep?