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Unformatted text preview: Function Fact Sheet Name of Function Famil : x o ‘ The general formula for this type of Describe how to determine if a given formula is this type of function? function (ifthere isone): 13‘, M o“ e¥?cwem+ M 3‘ game‘h‘ha w”, be +0 we
None. pow o? x. The simplest (parent) function of this type: 4..
4 H): 3 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 QS Other examples of formulas for this type of function: {'09: 1* {Kim 5L1“) x2 1 X
hiy§:‘::+ \r\L1)‘.‘5 (A
(b 1‘ v ‘5 U): ~1C'5ﬁ) 4:50 ‘— 9L6“? ‘U‘ 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 : NAlways DJsually DSometimes CINever Vertical Asymptote: Always CIUsually DSometimes DNever inﬂection points (changes from curving up to curving down or viceversa): DAlways UUsually USometimes [Shaver
Upper or Lower bounds on the range of the function: NAlways Cl Usually El Sometimes DNever Turns (changes from increasing to decreasing or viceversa) : Cl Always DUsually DSometimes NNever Continuous (can be drawn without lifting up your pencil) : EAlways [3 Usually DSometimes Cl Never Onetoone (passes the horizontal line test; has an inverse function) : 3 Always D Usually DSometimes DNever Always increasing OR Always decreasing: N Always Cl Usually [I Sometimes CINever Giveverbal description ofthe shape ofthegraphz‘flw. graph (“area/ﬁe; or aggreug£s on out. Side)
°t “Orn‘zokl‘ol Q$9MP+0+£ an “to. outer, am) apromkes What patterns are there in the outputs of this type of sequence? Check all that apply.
First Differences are Constant First Differences are constant for awhile and switch to the negative of the constant value. Second Differences are Constant but First Differences are not. Third Differences are Constant but Second Differences are not. \, Ratios or Ratios of First Differences are Constant
The patterns given above allow you to determine with absolute surety that a data set represents a specific type of function. However,
many functions have general patterns in their ﬁrst differences. If none of the above patterns are true of the function you are filling this
sheet out about, describe the general pattern you see in the first differences in the space below. (For instance, "The first differences are
small, then large, then small again”) Print an example data set from the function family spreadsheet used earlier, and put it immediately after this sheet. If this type of
function has any of the patterns listed above, make sure this is shown on your printout. Real World Applications List the real world applications of this type of function talked about on the Guide Sheet or in the lab.
For each application listed, indicate what real world quantity is the input and what real world quantity you get as an output.
Be very specific and give as many details of the application and its inputs and outputs as you can. Uﬂr€¢$fr€¢¥gb WPulaROV‘ %row H“ :hFuf“ kl“; 2V‘_PU+= ?6rula+\on
NOA'QV C Oolg‘hj “ “Pox : I r RaAtOOL‘ﬂme 6260“) “AP‘Aé' h‘ue Obird} :9/0 OF Motéﬂ‘a‘ leFl Other interesting facts about this type of function: $rw’f 4b.. show in) le boubltmj Wo'kg Exponential Functions: y = a (bx + c) + d Select: a=
b:
C:
d: x 1st Difference 2nd Difference Ratio of 1st Diff
1.011719
1 1023433 (101171875 1.011583
a 1.046875 00234375 001171875 1.0229008
1.09375 0.046875 0.0234375 1.0447761
1.1875 0.09375 0.046875 1.0857143
I 01875 009375 11578947
0375 01875 1.2727273
.13 0375 1.4285714
_i—§ 1.8571429
_a 19230769
mm
19795918
1.0m 1.9896907
mm 19948187
=] 19974026
19986996
.1 19993494
I ExponenﬁalFuncﬁons
50 
40 J
30 J
20
1O 1
I——_‘ T l T"? "I" e F— —'_‘ I 1’— l
10 8 6 4 —2 2 4 6 8 10
—10
20 
30 4
~40  ...
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 Spring '10
 Kennely
 Algebra, Limit of a function, Graph of a function, Asymptotic curve

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