Question

Write the coordinates of the image of the pont (-3,9) on the graph y=x^2 when each of the following transformations are applied:

a) a reflection in the x-axis followed by a vertical translation 4 units up

b) a vertical stretch by a factor of 1/3 about the x-axis

Answer 1

reflection: (x,y) -> (x,-y)
up 4: (x,y) -> (x,y+4)
so, (-3,9) -> (-3,-9) -> (-3,-5)

usually stretches are termed in the x- or y- direction
"about the x-axis?" Hmmm
If you mean stretched toward the x-axis (that is, in the y-direction), then (x,y) -> (x,y/3)
If you mean stretched along the x-axis (in the x-direction), then (x,y) -> (x/3,y)
Pick one, and plug in your numbers.