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# need help with function

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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.

(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