Chapter 1: Q77E (page 7)
77-78 Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.
77.
The graph of f is an odd function, and the graph of g is an even function.
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Sketch the graph of the function
\(g\left( x \right) = \left| {\left| x \right| - {\bf{1}}} \right|\)
In this section we discussed examples of ordinary, everyday functions: population is a function of time, postage cost is a function of package weight, water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.
In a certain country, income tax assessed as follows. There is no tax on income up to \(10,000. Any income over \)10,000 is taxed at a rate of 10%, up to an income of \(20,000. Any income over \)20,000 is taxed at 15%.
(a) Sketch the graph of the tax rate R as a function of the income I.
(b) How much tax is assessed on an income of \(14,000? On \)26,000?
(c) Sketch the graph of the total assessed tax T as a function of the income I.
Evaluate the difference quotient for the given function. Simplify your answer.
36. \(f\left( x \right) = {x^3}\), \(\frac{{f\left( {a + h} \right) - f\left( a \right)}}{h}\)
39-46 find the domain of the function.
44. \(f\left( u \right) = \frac{{u + 1}}{{1 + \frac{1}{{u + 1}}}}\)
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