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October 27th, 2016, 11:08 PM  #1 
Member Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0  Functions
Sketch f(x) = [2/(3x  1)] + 3 I know that the parent graph of the function is f(x) = 1/x and when I express the function of transformed graph, it is f(x) = [2/3(x  1/3)] + 3 I interpreted as the graph of f(x) = 1/x is moved 1/3 units to the right and it is narrower by 3 units, then it is moved 3 units upwards. Now my problem is, what effect does the 2 have on the graph? Last edited by skipjack; October 28th, 2016 at 02:09 AM. 
October 28th, 2016, 01:47 AM  #2  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
It falls into unclear/ambiguous/can't be determined, in part, because it looks as if it could be (2/3) multiplied by (x  1/3), (before adding the 3), which is not what you intend. Write them as: Sketch f(x) = 2/(3x  1) + 3 f(x) = 2/[3(x  1/3)] + 3                                       Take the 3 in the denominator out with the 2 as a fraction: f(x) = (2/3)*[1/(x  1/3)] + 3 $\displaystyle f(x) \ = \ \dfrac{2}{3}\left(\dfrac{1}{x \  \ \tfrac13}\right) + \ 3$ Then, you would not state it is "narrower by 3 units". Because 2/3 < 1, you state that the graph has a compression factor of 2/3. And you're correct that it has a horizontal right shift of 1/3 unit and a vertical up shift of 3 units. Last edited by skipjack; October 28th, 2016 at 02:09 AM.  
October 28th, 2016, 02:34 AM  #3 
Member Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0 
It makes sense now. Thnaks very much Sir 
October 28th, 2016, 03:08 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,053 Thanks: 1395 
That should be a vertical compression factor of 2/3, applied prior to the vertical shift.


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