I would also like to know the answer to this. Mostly for review.

https://web2.0calc.com/questions/functions-help_18

stressedmathkid123 May 9, 2021

#1**+1 **

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 = -3f(3(x+2))-2?

The 2 in "x+2" horizontally shifts f(x) to the left by 2 units, so it becomes (a-2, b)

the 3 in "3(x+2)" horizontally shrinks f(x) by a factor of 3, so it becomes ((a)/3-2, b)

the -3 in "-3f(3x+6)" vertically stretches f(x) by a factor of -3, so it becomes ((a)/3-2, -3b)

lastly, the -2 in "-3f(3x+6)-2" vertically shifts f(x) down by 2 units, so it becomes \(\displaystyle \boxed{\left(\frac{a}{3}-2, -3b-2\right)}\)

textot May 9, 2021

#2**+1 **

Since +2 shifts f(x) to the left by 2 units, shouldnt that be (a+2,b) instead of (a-2,b) which results in the solution of (a/3+2, 3b-2)?

Edit: wait, it's supposed to be (a/3-2, 3b-2) because the -3 flips f(x) across the x axis right?

stressedmathkid123
May 10, 2021