Suppose(8,6) is a point on the graph of y=​g(x).

Question

​(b) What point is on the graph of ​y=-4g(x-4)+2?

I just know you go up 2 and right 4 but I don't know what to do with the -4 and if you could show me so I can understand the other problems! I kind of forgot about transformations

Answer 1

shift right 4
stretch by 4 vertically
reflect across the x-axis
shift up 2
(x,y) → (x+4,y) → (x+4,4y) → (x+4,-4y) → (x+4,-4y+2)
so (8,6) → (12,-22)

consider g(x) = x/2 + 2
the transformed function g'(x) = -4((x-4)/2 + 2)+2
g'(12) = -4(4+2)+2 = -22

Answer 2

Suppose is a point on the graph of y​g(x).
​(a) What point is on the graph of ​?
​(b) What point is on the graph of ​?
​(c) What point is on the graph of ​?