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?

Guest Nov 13, 2021

#1**+1 **

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)

hectictar Nov 13, 2021