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If points (a,b) are on the graph of y = f(x), what points must be on the graph of y = -3f(3x+6)-2?

 Nov 13, 2021
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Since  (a, b)  is on the graph of  y = f(x),  we can say that:   f(a) = b

 

Let's plug in (a-6)/3  for  x  into the equation for the second graph.

 

y  =  -3 * f( 3 [ (a-6)/3 ] + 6)  -2   =   -3 * f(a) - 2   =   -3b - 2

 

When  x = (a-6)/3 ,  y = -3b - 2  so we can say that the point  \((\frac{a-6}{3}, -3b-2)\)  must be on the second graph.

 

 

Check: https://www.desmos.com/calculator/aqfexnjff4

 

(On that graph we can move a around and also change the definition of  f , and for each the cases I tried this seems to hold)

 Nov 13, 2021

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