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Function Notation

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Saraf santhosh kumar
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60 views7 pages

Function Notation

Uploaded by

Saraf santhosh kumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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sar vz01 Function Notation If fx) 3x ~ 10, what is f(-5x) equal to? A) 15x-10 B) -15x—10 ©) 15x+10 D) 15x° + 50x ‘Unauthorised copying or eure of any part of hi pages 457 FUNCTION ( fC ‘ IN): " often look more onthe left side } an equation with » side, but with, eat fix), Because function: iy teplaced with, tions are essentially just proberns ly are. equations they can x can easily be graphed. Function Pid thon they actual complicats Remember, Function inat to do wi it tells you 1 Once Yo get te “output! jpet 0 recipe ith the "put © (Ee) © Six) =4x +2 cog «34-1 tx +2 means th m8, re the same thing as y sr +2. Thatmeansyoucan even graph ay asyou ordinary would Ths gve us 0 Function they hel cour recipe 9079 1° ipsa ton when you need rrultiply the input Storer haencon non te boy negetve 3 then separ euten. baron like euotract 10 \gihertometingtvthatomat EIT Iffx) =~ If fx) = ~3x ~ 10, what is f{-Sx) equal to? @ ss-10 1 ro get H'sornething) pot B) -I5x-10 jog that ‘something Fe the Function everywhere © 15x+10 there's an py 1522 +500 Here, ‘something ® % °° al we 5x into Out howe +0 do 6 PL Function everywnere we have an % £Gd = 3x - 0 plas = 35% - 10 Psd = GD And, there's your answer: 458 7 FUNCTION, FUNCTION, WHAT'S YOUR... FUNCTION? ‘Afunction is just a series of steps for you to perform. That's all. it may help you to think of a function as a button on your calculator. Ifyou type a number into your calculator and then hit the "squared" button, it performs a function. Your calculator multiplies whatever number you gave it by that same number. You could think of the "squared” button as performing the function fix) =. ‘What if your calculator had a “g(x)" button? That button would also be a function, but what would it do? Well, that all depends on what g(x) is defined as. If gx) is defined as g(x) =.x°~ 4, then that's what the g(x) button would do. It would take whatever number you punch into the calculator, square it, and then subtract 4 from the product. Obviously, the end result will depend on what number you punch into the calculator before hitting the g(x) button. That's what makes it a function! ‘That's really all you're doing on an SAT function problem. The problem will usually give you the definition of. the function, meaning a list of steps to perform. Then the problem will ask something like "What is the value of f(x) when x= 5?" All you need to do is plug in 5 for x and solve for flx) as fit were any other variable. ftx) Is basically just a stand-in fory, afterall lifts) =1°+ 3, then 4) = This statement basically tells you to take the number in the parentheses after the fand plug it in wherever you see an.x. Put it into the equation wherever you see an x and solve for /\d) as it were the variable y. fia) = (AY + 344) fay= 64412 fia) =76 Hoy WHATEVER YOU FIND IN THE PARENTHESES IS WHAT YOU PLUG IN FOR X Plug in whatever isin the parentheses for x,no matter what its! & Ifyou'te asked to find (5)? Use (5) in place of x. Simple, right? If you're asked to find fle + 1)? Plug in (x + 1) Stil pretty simple. Ifyou're asked to find hamburger)? Plugin the word (hamburger) in place of x. Remember to keep parentheses around whatever you plug in for x because it represents one number. sar vz01 ‘Unauthorized copying or reuse of any part ofthis page ga. 459 c ABASIC FUNCTION IS LIKE A MICROWAVE 5 f(x) machine x burr it THEN, YOU RUN IT THROUGH AGAIN! F(x) f(x) machine f(x) machine A FUNCTION WITHIN A FUNCTION IS LIKE MICROWAVING SOMETHING TWICE re Sx) So) AFUNCTION WITHIN A DIFFERENT FUNCTION IS A LOT LIKE DOING LAUNDRY /flx) washing machine O00 x Sx) comes a burch 4 dct clot wasting wach FUN WITH FUNCTIONS 1. Mffix) = 3x+ 6 and g(x) = -2x~2 for all values 3. ffx) =2e+ 10 and g(x) =2° ~ 4 for all values of ‘ofr, what isthe value of g((2)? +x, what is the value of e((x)) ~ flg(2))? 2. Ife) =3 = 4eand g(x) = 2+ forall valuesof 4, ffx) =2e = and g(x) =2 = 2 forall values 4, what is the fig(3))? of.x, what is the value of (@(/(3)))? sar vz04 ‘Unauthorized copying or reuse of any part ofthis page ga. 462 GRAPHING A FUNCTION It's helpful to think of the graph ofa function as the value of the “output” (the y-value) for every input" (the x-value). To graph a function, just replace fix) with y and graph the function like you ‘would any other equation. fo) =2x+1 x | READING THE GRAPH OF A FUNCTION Sometimes they'll give you the graph of a function, but not the actual function. Here, you just have to work backwards. For any "x" (the x-coordinate),fix)= the y-coordinate. a _ (23) or fe) f-2=3 a what the We have no idea x equation For FOx) 1s, bat We ed Prom the aR that iF x = -2 then £00 = 3. YOUR TURN = ® Here's the graph of a function gis. Use the graph to answer the following questions. 1, What is (4)? What's a value of x for which g(x) = -3? For how many values of x, where -4.

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