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Unformatted text preview: Function Fact Sheet Name of Function Family: I: ego. High“; 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): The simplest (parent) function of this (1) 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? [03 NO) 55* i~+ arw‘l‘er “nan ZQVO +0 ‘PI‘MJ 'H‘tﬁ Jamaﬁn Other examples of formulas for this type of function: , f(4\\1_"\l031(1l‘l3‘\ may. iogzbo km: 3103 L Lr~4>+7
Z (503121033043H I My.) >‘liALYxlZ.\ ‘3 3(¥§:l03eC1)= h 9(ch '‘ l.ln(¥ ~51) 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):
Horizontal Asymptote : CIAIways [Usually DSometimes Never Vertical Asymptote: EAlways DUsually 8 Sometimes I] Never lnflection points (changes from curving up to curving down or viceversa): DAlways DUsually USometimes Niever
Upper or Lower bounds on the range of the function: DAlways CI Usually N Sometimes CINever Turns (changes from increasing to decreasing or viceversa) : D Always DUsually DSometimes SNever Continuous (can be drawn without lifting up your pencil) : SLAiways Cl Usually El Sometimes El Never Onetoone (passes the horizontal line test; has an inverse function) : l3 Always [:1 Usually DSometimes DNever Always increasing OR Always decreasing: 8 Always U Usually El Sometimes [Never
Give verbal description of the shape of the graph: Tl Forms CL (virth \i‘ne wt‘th a Vtvtt‘cal Rainy/of! 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, "The first differences are
small, then large, then small again”) W 0? \M) Aiﬁ‘ﬁvmcte 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.
\Quwlwo) WNQ inpu‘i‘v ’i’"j
cu‘r‘pu’r — F” F" ' “’5 Rid/Jed ﬁmlt Yaiw‘vng  rotRug is We GuiFuheovi/(‘qwkt Power ’19 “he “PA Other interesting facts about this type of function: QOU'N II II II II Ratios ——_
_————
———
——_ 422877
1 5.64386 1 3.643 I I
—I 1: 0.35614 ll
AM A 1.169925001 1.389975
0.830074999 1.1990623
0.64385619 1.1287712
6.169925 0.526068812 1.0932109
6.61471 0.444784843 1.0720892
7 0.385290156 1.0582475
7 7.33985 0.339850003 1.04855
7.643856 0.304006187 1.0414186
7.918863 0.275007047 1.0359775
10 8.169925 0.251061764 1.0317043 8.400879 0230954435 0.0201073291.0282689 4.16992 5.643856 , , 12 8.61471 0.2.1.3.830408. , ~0.01?124027.,.1.0254.53,3, , Logarithmic Functions
10 10 5 ...
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 Spring '10
 Kennely
 Algebra

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