Where is the point (3,-1) translated to after a vertical stretch of 4, a reflection in the x-axis and a horizontal shirt left by 2?
start with (3,-1)
if we make a vertical shift, we are changing the y-value. making a shift of +4 is moving up 4 units, so our point becomes:
(3, -1 + 4) = (3 , 3)
now, reflecting in the x-axis is a vertical shift. it's shifting down twice the amount of units we are above the x-axis. you can play around with a graph to see this
so for reflection in the x-axis, we change the y-value to negative, so our point becomes
(3, -3)
a horizontal shift is changing the x-value. changing by 2 is adding or subtracting 2 from the x-value. if you shift to the right, you add, if you shift to the left you subtract. shifting 2 units, i will assume it's to the right
so our point becomes
(3 + 2, - 3) = (5,-3)