April 6th, 2018, 11:21 AM  #1 
Newbie Joined: Apr 2018 From: Chile Posts: 3 Thanks: 0  Function problem
If you can help me please, the correct answer is E, but if you can explain why the 3 sentences are correct I would appreciate it very much. Thanks. Funciones.jpg Last edited by skipjack; April 6th, 2018 at 12:41 PM. 
April 6th, 2018, 01:53 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
The diagram is badly drawn. It should appear more like as shown below. ABgraph.PNG OB has slope 1/2 and OA has slope 2, where A is the point (3, 6) and B is the point (6, 3). 
April 27th, 2018, 04:44 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,159 Thanks: 866 
I agree that the picture is badly drawn or at least badly labeled. Also, we must assume that OA and OB are straight lines, which is not stated. IF OA is a straight line through (0, 0) and (2, 4) then f(x) = 2x for x < 0 so that f(3) = 2(3) = 6. IF OB is a straight line through (0, 0) and (4, 2) then f(x) = x/2 for x > 0 so that f(6) = 6/2 = 3. Knowing that A = (3, 6) and that B = (6, 3) we can calculate the lengths of the sides: $\displaystyle OA= \sqrt{(3)^2+ 6^2}= \sqrt{45}= 3\sqrt{5}$, $\displaystyle OB= \sqrt{6^2+ 3^2}= \sqrt{45}= 3\sqrt{5}$. Triangle AOB is an equilateral triangle with sides OB and OA congruent.
Last edited by skipjack; April 27th, 2018 at 06:40 AM. 
April 27th, 2018, 06:33 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
I assume you mean "isosceles right triangle", not "equilateral triangle".


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