How do you transform a graph of y=g(x) to y= g(2x)+ 3 (the coordinates are (-2,4)(0,0)(4,2)?

Question

How do you transform a graph of y=g(x) to y= g(2x)+ 3 (the coordinates are (-2,4)(0,0)(4,2)? I don’t understand.

How do you transform graph y = f(x) to graph y= -f(x)-1 ? (The coordinates are (0,0) (2,4) (4,0)

Answer 1

For y = g(2x)+3

g(2x): For the x-coordinate transformations, you do the opposite of what it reads. So divide every x-coordinate by 2 making the points: (-1, 4) (0, 0) (2, 2)

g(2x) + 3: Add 3 to each y-coordinate so the points become: (-1, 7) (0, 3) (2, 5)

For y = -f(x) -1

-f(x): Multiply the y-coordinate by -1: so the points become (0,0) (2,-4) (4,0)

-f(x) - 1: Subtract 1 from every y-coordinate so the points become: (0,-1) (2,-5) (4,-1)