Write a function for the graph described as a transformation of y=x^2. 1. y=x^2 experiences a vertical stretch of factor 2 and then a shift right of 3 units. 2. y=x^2 experiences a shift left by 2 units, then a horizontal shrink factor of 1/2, then a shift down of 5 units. 3. y=x^2 experiences a shift to the right 1 unit, is stretched vertically by a factor of 1/2, then is shifted down 4 units. 4. y=x^2is reflected across the x-axis, stretched vertically by a factor of 3, and shifted left 7 units.

we are given

parent function as

(1)

vertical stretch of factor 2

so, we can multiply y-value by 2

then a shift right of 3 units

so, we can replace x as x-3

(2)

a shift left by 2 units

we can replace x as x+2

then a horizontal shrink factor of 1/2

so, we can multiply by 2 to x-value

then a shift down of 5 units

we can subtract y-value by 5

so, we get

(3)

a shift to the right 1 unit

we can replace x as x-1

stretched vertically by a factor of 1/2

we can multiply y-value by 1/2

then is shifted down 4 units

we can subtract y-value by 4

(4)

reflected across the x-axis

we can multiply y-value by -1

tretched vertically by a factor of 3

multiply y-value by 3

shifted left 7 units

we can replace x as x+7