Unformatted text preview: 50 CHAPTER 1 FUNCTIONS AND MODELS 3. (a) An even function f satisﬁes f(~:£) = f(m) for every number x in its domain. It is symmetric with respect to the y—axis. (b) An odd function 9 satisﬁes g(—a:) = —g(m) for every number x in its domain. It is symmetric with respect to the origin. 4. A function f is called increasing on an interval I if f(a:1) < f($2) whenever 301 < :02 in I. 5. A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon. 6. (a) Linear function: f(m) : 230 + 1, f(a:) : aw + b 7.
(b) Power function: f(:t) : £62. f(m) : m“
(c) Exponential function: f(a:) : 2“”, f(a:) : a2
(d) Quadratic function: ﬂan) = m2 + x + 1,
f(ZE) : c1302 +bw+c
(e) Polynomial of degree 5: f(av) : 3:5 + 2
m I lei :c
93+2‘ where (f) Rational function: f (:0) = P(w) and Q($) are polynomials 8. (a) _ (b) (d) (e) (f) (h) ...
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- Spring '10