Transformation Function

Question

If the point (-3,2) lies on the graph of y=f(x), use the transformation theorem to find the point on the graph of the transformed function

a) y=-3f(x-3)+2.5

b) y=f(2x+1)-3

Answer 1

a) y=-3f(x-3)+2.5

1. move to the RIGHT by 3 (means add 3 to each X point)
2. stretch vertically by mult. of 3 (each Y point will go 3 times higher/lower, visually)
3. flip it 'upside down (because of the negative sign, your positive Ys become negative)
4. move UP by 2.5
5. Or, use Desmos for such visual understanding

Answer 2

1. Remember their is 4 kinds of transformations, there is translation, dilation, rotation and reflection.
2. This is a rotation type of transformation look at the integer signs.
3. Draw the graph