Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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3 2 1. Factor fully the polynomial function: g(x) = 30x-53x+31x-6 For the function state: the x-intercept(s) (you need to factor the functions) the y-intercept the end behaviour any symmetry the number of turning points and their approximate location the type of each turning point (local or absolute, max. or min.) (If you can not find some item, then state why not) Make a graph of the function and clearly label all the features. 2.a) A function has exactly 3 zeroes; they are -1, 0, and 2. The function passes through the point (1,6). Sketch the function. Find the equation of the function. b) A 4th degree function has minima at (-3,-6) and (3,-6) and a y-intercept at (0,3). Sketch the function. Find the equation of the function. (HINT: If the minima were on the x-axis then this would be easy. How can you move them? WARNING: a question like this may be on the test and/or summative. Make sure you know how to do it.)
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Transcribed Image Text:3 2 1. Factor fully the polynomial function: g(x) = 30x-53x+31x-6 For the function state: the x-intercept(s) (you need to factor the functions) the y-intercept the end behaviour any symmetry the number of turning points and their approximate location the type of each turning point (local or absolute, max. or min.) (If you can not find some item, then state why not) Make a graph of the function and clearly label all the features. 2.a) A function has exactly 3 zeroes; they are -1, 0, and 2. The function passes through the point (1,6). Sketch the function. Find the equation of the function. b) A 4th degree function has minima at (-3,-6) and (3,-6) and a y-intercept at (0,3). Sketch the function. Find the equation of the function. (HINT: If the minima were on the x-axis then this would be easy. How can you move them? WARNING: a question like this may be on the test and/or summative. Make sure you know how to do it.)
3. Find the asymptotes of the following rational function, q(x). Find its asymptotes. If it does not have a particular type of asymptote (vertical, horizontal, or oblique) then briefly say why it does not. 5x -1 q(x) = x´ - 2x – 3 Describe the end behaviour of the function. Find its intercepts. Make a graph of the function. Draw and label the asymptotes and other features. 4. Abel needs x minutes to package a case of 24 widgets. Brian can fill a case in 3 minutes less time than Abel. Working together, they can fill a case in 12.32 minutes. How much time does Abel need when he is working alone? [Hint: How many widgets can Abel, Brian, or the team package in one minute?]
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Transcribed Image Text:3. Find the asymptotes of the following rational function, q(x). Find its asymptotes. If it does not have a particular type of asymptote (vertical, horizontal, or oblique) then briefly say why it does not. 5x -1 q(x) = x´ - 2x – 3 Describe the end behaviour of the function. Find its intercepts. Make a graph of the function. Draw and label the asymptotes and other features. 4. Abel needs x minutes to package a case of 24 widgets. Brian can fill a case in 3 minutes less time than Abel. Working together, they can fill a case in 12.32 minutes. How much time does Abel need when he is working alone? [Hint: How many widgets can Abel, Brian, or the team package in one minute?]
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