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1
FUNCTIONS AND MODELS
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1.1 Four Ways to Represent a Function
In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here. 1. (a) The point (?1, ?2) is on the graph of f , so f (?1) ¡ë ?2.
(b) When x ¡ë 2, y is about 2.8, so f (2) ? 2.8. (c) f (x) ¡ë 2 is equivalent to y ¡ë 2. When y ¡ë 2, we have x ¡ë ?3 and x ¡ë 1. (d) Reasonable estimates for x when y ¡ë 0 are x ¡ë ?2.5 and x ¡ë 0.3. (e) The domain of f consists of all x-values on the graph of f . For this function, the domain is ?3 ¡Â x ¡Â 3, or [?3, 3]. The range of f consists of all y-values on the graph of f . For this function, the range is ?2 ¡Â y ¡Â 3, or [?2, 3]. (f ) As x increases from ?1 to 3, y increases from ?2 to 3. Thus, f is increasing on the interval [?1, 3].
3. From Figure 1 in the text, the lowest point occurs at about (t, a) ¡ë (12, ?85). The highest point occurs at about (17, 115).
Thus, the range of the v¡¦(»ý·«)