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Logistic fact sheet - Function Fact Sheet Name of Function...

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Unformatted text preview: Function Fact Sheet Name of Function Famil : Lo ‘ f The general formula for this type of Describe how to determine if a given formula is this type of function? function (if there is one): a Vom'ub le an the ‘00 How "5 +0 five, Fawe, 0P 4 Va lue of ‘ q Y2F£*3U‘¥B€(¥+D x The simplest (parent) function of this W \ pe: _ (3 ($3 : \fi-QTY What other names does this type of Is the domain of this type of function always all real numbers? If not, how do you find the function go by? domain? \I [I‘MF+Q) €16)an {‘tkd‘ 1'15 Other examples of formulas for this type of function: htshfifln ‘8 HA: loo \ * e: . +n?e'°$* t5(y)=£.9._ -7 ca): 2.10 ‘vflx {-— “2-6 He“ Sketch below all the possible shapes that you discover this kind of function can have. Graphs Continued For each listed property indicate whether the graph of this function has that property always, usually, sometimes, or never (describe the exceptions if there are any): Horilontal Asymptote : ELAlways DJsuallv DSometimes DNever Vertical Asymptote: DAlways DUsually C] Sometimes ElNever lnflection points (changes from curving up to curving down or vice-versa): UAlways DUsually DSometimes Evever Upper or Lower bounds on the range of the function: SAlways D Usually [I Sometimes DNever Turns (changes from increasing to decreasing or vice-versa) : D Always DUsually DSometimes ENever Continuous (can be drawn without lifting up your pencil) : EAlways Cl Usually [3 Sometimes D Never One-to-one (passes the horizontal line test; has an inverse function) : 8 Always Cl Usually USometimes DNever Always increasing OR Always decreasing: & Always Cl Usually Cl Sometimes CINever Giveverbal description ofthe shape ofthegraph: fink?“ ‘mutases or Atovta‘ses “‘53)? .‘n 1,“: Mtge“ am; 5'4.)le 0H loo‘l'l/i ends. What patterns are there in the outputs of this type of sequence? Check all that apply. First Differences are Constant First Differences are constant for awhile and switch to the negative of the constant value. Second Differences are Constant but First Differences are not. Third Differences are Constant but Second Differences are not. Ratios or Ratios of First Differences are Constant The patterns given above allow you to determine with absolute surety that a data set represents a specific type of function. However, many functions have general patterns in their first differences. If none of the above patterns are true of the function you are filling this sheet out about, describe the general pattern you see in the first differences in the space below. (For instance, "T he first differences are small, then |arge,thensmallagain.") pmpufmfi Owe V997 lang ,‘n “Hat M.‘JJlfl)anb smdfl on e.an 9. Print an example data set from the function family spreadsheet used earlier, and put it immediately after this sheet. If this type of function has any of the patterns listed above, make sure this is shown on your printout. Real World Applications List the real world applications of this type of function talked about on the Guide Sheet or in the lab. For each application listed, indicate what real world quantity is the input and what real world quantity you get as an output. Be very specific and give as many details of the application and its inputs and outputs as you can. FOFUIA‘LI‘OA grow-‘4‘ : ‘q‘Me OU+PU+: POPUIQJ‘I'UH bi$€ase five“) Inpul-Z Mme Ov‘l‘PU‘l’l Inflected Fear/e, Other interesting facts about this type of function: “as Lao-H" U FPer aw) lo M! e/ (00¢,sz ea (’7 {1 'MG Logistic Functions: y = _cx + d 1 + be Select: 7 ” l _—_— ——__ __—— ——__ --—_ 1—— -3_ - - 2-039014 - 2-199071 m 2054982 1 .700337 2 1357739 3 115301 1059841 1022536 1008363 7 1003087 1001137 1000418 10 151 0854 0 079808363 , -0 040152444 0 068775317 1 000154 LogistilsJ Functions 200 150 - 100 50 -100 ‘ -150 —200 ‘ -250 ...
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