Chapter 1: Q4E (page 7)
3-16 A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.
\(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
\(f\left( x \right)\) | 1.0 | 1.9 | 2.8 | 3.5 | 3.1 | 2.9 |
The function is one-to-one.
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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.
65-70 Find a formula for the described function and state its domain.
A rectangle has perimeter 20m. Express the area of rectangle as a function of the length of one of its sides.
Determine whether f is even, odd, or neither. You may wish to use a graphing calculator or computer to check your answer visually.
83. \(f\left( x \right) = \frac{x}{{x + {\bf{1}}}}\)
7-14 Determine whether the equation or table defines y as a function of x.
\({x^{\bf{2}}} + {\left( {y - {\bf{3}}} \right)^2} = {\bf{5}}\)
The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; t is measured in hours starting at midnight.)
(a) What was the power consumptions at 6 AM? At 6 PM?
(b) When was the power consumption the lowest? When was it the highest? Do these times seem reasonable?
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