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Chapter 3: Q. 103 (page 158)
Can a quadratic function have a range of ? Justify your answer.
No there does not exist a quadratic function whose range is of whole real numbers
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Suppose that the manufacturer of a
gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is
What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?
Graph the function by starting with the graph of and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.
Hint: If necessary, write in the form .
A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars).
(a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.
(b) The quadratic function of best fit to these data is
Use this function to determine the optimal level of advertising.
(c) Use the function to predict the total revenue when the optimal level of advertising is spent.
(d) Use a graphing utility to verify that the function given in part (b) is the
quadratic function of best fit.
(e) Use a graphing utility to draw a scatter diagram of the data and then graph the quadratic function of best fit on the scatter diagram.
A projectile is fired at an inclination of to the horizontal, with a muzzle velocity of . The height h of the projectile is modeled by
where x is the horizontal distance of the projectile from the firing point.
Part (a): At what horizontal distance from the firing point is the height of the projectile a maximum?
Part (b): Find the maximum height of the projectile.
Part (c): At what horizontal distance from the firing point will the projectile strike the ground?
Part (d) Using a graphing utility, graph the function h, .
Part (e): Use a graphing utility to verify the results obtained in parts (b) and (c).
Part (f): When the height of the projectile is above the ground, how far has it traveled horizontally?
Under what circumstances is a linear function odd? Can a linear function ever be even?
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