Ex 1-4 - | t. gG) = rf d. .(r) = 8' b. c(,) = 5, d. R@-1? b...

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1.4 Identifying Functions; ilathematjcal llodels 37 law we canDot prove or verify a theorcm byjust looking at some examples. Nevertheless, Figue 1 .49 suggests that Kepler's third law is r€asonable. . The concept of proportionality is on€ way to test the reasoMbleness ofa conjectued relationship between two variables, as in Example 3. lt can also provid€ the basis for an empiric|l model which comes entirely ftom a table ofcollect€d data. Recognizing Functions ln Exercises I 4. identit each fiDction d a @nstant finctiot, linear fimction, pos€r tunction, polynomial (state its degree), ratiotal fibc' lion. alsebraic finctron. lrigonomerric irction, exponential functio4 or logarithmic funcrid. Rddber that sone irctions car felL into mo.e oan one csreSory 6.r. l=5t b. l=:' r. a. lG)=7-3x c t/k)= V:'+ |
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Unformatted text preview: | t. gG) = rf d. .(r) = 8' b. c(,) = 5, d. R@-1? b !=x'tz-\c+l c. s(r) = 2rA d. In Exrcises 5 and 6. maich each equatio! with it3 graph. Do nol use a graphing device, and giv reasons fo. you 6wei Increasing and Decreasing Functions Gnph the imctions in Exercises 7 18. l\7lBt s)mehi$, if any, do the gnphs hae? Specit the inl,enals Nd which the tunction is in-creasiry dd the iniervak whe.e it is decreding. t1+t *'(;.';) l@= s r = -] tv=*Q) 13. J' = rr/8 15. y = x)/' 17. t = (-x)'1tl s, r,=-+ 10. v=-! 12. y=lt M. y= ali 16. r=( xlt'z 18. ), = -t2tt Even and odd Functions In Exe.cises 19 30, say whdhr tle tunction is evd, od4 or neiihe. . Give rcasoN for you dMr. le. l(x) = 3 2r.JG)=,'z+1 23. s(r) = 13 + r 20. 11;"") = t-22. l\x) = x2 + r 24. s(x) = ,a + 3r2 - |...
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