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Chapter 2: Problem 6
Find the domain of each rational function. $$h(x)=\frac{x+8}{x^{2}-64}$$
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Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2}>0$$
The rational function $$f(x)=\frac{27,725(x-14)}{x^{2}+9}-5 x$$ models the number of arrests, \(f(x),\) per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver's age, \(x\). a. Graph the function in a [0,70,5] by [0,400,20] viewing rectangle. b. Describe the trend shown by the graph. c. Use the \([\mathrm{ZOOM}]\) and \([\mathrm{TRACE}]\) features or the maximum function feature of your graphing utility to find the age that corresponds to the greatest number of arrests. How many arrests, per 100,000 drivers, are there for this age group?
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{(x-3)^{2}}+2$$
Galileo's telescope brought about revolutionary changes in astronomy. A comparable leap in our ability to observe the universe took place as a result of the Hubble Space Telescope. The space telescope was able to see stars and galaxies whose brightness is \(\frac{1}{50}\) of the faintest objects observable using ground-based telescopes. Use the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from an observer to show that the space telescope was able to see about seven times farther than a groundbased telescope.
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x^{2}}-4$$
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