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43 Hello, I appreciate you volunteering and taking the time to help others.  I'm studying for the ACTs and I could use a tad bit of help.

My question is: if I have a function y = f(x) containing the points (2,6) and (5,-4). Then, name two points in the function g if g(x) = -3f(x+2).

The book I have is just of practice problems and only gives the answer, not the step-by-step instruction. I haven't been able to get this one, so I was hoping you could assist.

If you could solve this problem and show me how you did it, it would be a big help. Thank you, Reggie.

Hopefully your function f is a line and if it is you find the slope m using the two points and then use the slope and one of the points to find an equation, I.e., the function f.

(2, 6), (5,-4)  m = (y2-y1)/(x2-x1) ~~> (-4-6)/(5-2) = -10/3
Now use y-y1=m (x-x1)~~> y-6=(-10/3)(x-2)~~> y=(-10/3)x+20/3+6 or y=(-10/3) x+38/3
-3f (x+2)=-3(-10/3 (x+2)+38/3) ~~>-3 (-10/3) (x+2)-3 (38/3)~~>10 (x+2)-38~~>10x+20-38
g (x)=10x-18
Choose any two values of x to find the corresponding values of y and you have your two points
Let x=0, then y=10 (0)-18=-18 and one of your points is (0,-18) and let x=1, then y =10 (1)-18=-8
so your second point is (1,-8)

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