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Unformatted text preview: Function Fact Sheet Name of Function Family: Abglgle Vglug The general formula for this type of Describe how to determine if a given formula is this type of function? There if: on alp‘mlvl'e Valoelw the ‘Fuvidi'an function (if there is one): None The simplest (parent) function of this
‘1 = My) = *\ 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 80 by? domain? Wyn alasolv l-e 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 : DAlways DJsually DSometimes [SNever Vertical Asymptote: CIAlways DUsually C] Sometimes N Never lnﬂection points (changes from curving up to curving down or vice-versa): EAlways UUsually DSometimes SNever Upper or Lower bounds on the range of the function: Eklways [3 Usually C] Sometimes DNever one or We after) mf /
Turns (changes from increasing to decreasing or vice-versa) : N Always DUsually DSometimes UNever
Continuous (can be drawn without lifting up your pencil) : NAlways [:1 Usually D Sometimes El Never
One-to-one (passes the horizontal line test; has an inverse function) : El Always D Usually DSometimes ENever Always increasing 0R Always decreasing: I] Always U Usually El Sometimes NNever Give verbal description of the shape of the graph: 1» looks like or ﬂv“ 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”) i“} b:‘r‘¥. m We 6M“)th We, 6wi‘l'ok 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. MWlMN Miami a’l Bro Costs out as T‘l’ bot/me; an line can"). thuic=¥fMQ ouﬁottbigl- a k? a“ k lea“ loounu‘uﬁ o (if a wall. Iwrul't +l\W\'€ Output: Dr‘sfauce t
3 Absolute Value Functions: y=a|x + b + c Absolute Value Functions 1st Difference 2nd Difference Ratios 10 201 15% 10J -10 -1o 4 -15 a -20 _ ...
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- Spring '10
- Algebra, Continuous function, Limit of a function