Suppose(8,6) is a point on the graph of y=g(x).
(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
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
Suppose is a point on the graph of yg(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 ?
To find the point on the graph of y = -4g(x-4) + 2, when you have a point (8,6) on the graph of y = g(x), you can follow these steps:
Step 1: Apply the horizontal transformation:
Since there is a (x-4) inside the function, the graph of y = g(x) will shift 4 units to the right. So, start by subtracting 4 from the x-coordinate of the given point (8,6). This gives us the new x-coordinate: 8 - 4 = 4.
Step 2: Apply the vertical transformation:
Next, we have -4g(x-4). The -4 outside the function means that the graph will be reflected vertically, and the factor of 4 indicates that it will be scaled vertically by a factor of 4. To apply this transformation, multiply the y-coordinate of the given point (6) by -4, giving us -4 * 6 = -24.
Step 3: Apply the vertical shift:
Finally, we have -4g(x-4) + 2. The +2 outside the function means that the graph will shift vertically 2 units up. To apply this vertical shift, add 2 to the result obtained in the previous step (-24 + 2 = -22).
Therefore, the point on the graph of y = -4g(x-4) + 2, corresponding to the point (8,6) on the graph of y = g(x), is (4, -22).