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Section 2.1

Please post comments if you find any errors, or if you wish to contribute answers for additional problems. You may find information on using \LaTeX here.

1. (a) y is a function of x
Relationship: y = 2x
Domain = [0, S] , where S is the maximum speed of the train
Range = [0, 2S]

(c) y is a function of x
Domain = [0, 8760] , in hours
Range = [221.5, 238.9] , in thousands of miles

(d) y is not a function of x

(f) y is a function of x
Relationship: y = 2\sqrt{\pi x}
Domain = (0, \infty)
Range = (0, \infty)

(g) y is a function of x
Relationship: \displaystyle{y = \begin{cases}41,& \text{if } 0 < x \le 1,\\ 58,& \text{if } 1 < x \le 2,\\ 75,& \text{if } 2 < x \le 3,\\ 92,& \text{if } 3 < x \le 3.5, \end{cases}} with x in ounces and y in cents (as of 14 May, 2007)
Domain = (0, 3.5]
Range = \{41, 58, 75, 92\}

3. (a) (-\infty, \infty)

(c) \{t : t \le -3 \text{ or } t \ge 2\}

(e) \{s : s \ne -3, s \ne 3\}

(g) \{s : s < -3-2\sqrt{2} \text{ or } s > -3 + 2\sqrt{2}\}

4. (a) f \circ g(x) = 20x + 4 , g \circ f(x) = 20x + 58 , f \circ g(3) = 64 , g \circ f(3) = 118

(c) \displaystyle{f \circ g(x) = \frac{6x - 55}{(x - 9)^2}}, \displaystyle{g \circ f(x) = -\frac{1}{x^2 - 6x + 9}}, \displaystyle{f \circ g(3) = -\frac{37}{36}}, g \circ f is not defined at 3

9. (a) Domain = (-\infty, \infty)
Range = \{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}

(b) Domain = (-\infty, \infty)
Range = \{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}

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