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Chapter 4: Q. 10 (page 224)
True or False The graph of a rational function may intersect a vertical asymptote.
The given statement " The graph of a rational function may intersect a vertical asymptote." is false.
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In Problems 49鈥� 60, for polynomial function
(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(c) Determine the maximum number of turning points on the graph.
(d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of .
Hurricanes In 2005, Hurricane Katrina struck the Gulf Coast of the United States, killing 1289 people and causing an estimated $200 billion in damage. The following data represent the number of major hurricane strikes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.
(a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the
two variables.
(b) Use a graphing utility to find the cubic function of best fit that models the relation between decade and number of major hurricanes.
(c) Use the model found in part (b) to predict the number of major hurricanes that struck the Atlantic Basin between 1961 and 1970.
(d) With a graphing utility, draw a scatter diagram of the data and then graph the cubic function of best fit on the scatter diagram.
(e) Concern has risen about the increase in the number and intensity of hurricanes, but some scientists believe this is just a natural fluctuation that could last another decade or two. Use your model to predict the number of major hurricanes that will strike the Atlantic Basin between 2011 and 2020. Is your result reasonable?
What is the length of the edge of a cube if its
volume could be doubled by an increase of centimeters in
one edge, an increase of centimeters in a second edge, and
a decrease of centimeters in the third edge?
Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.
Field Trip Mrs. West has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular \( 40 price of the ticket by \) 0.20 for each ticket sold. The cost of the bus, \( 500, will be split equally among each of the students. How many students must attend to keep the cost per student at or below \) 40?
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