Question

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.

Answer 1

B

Explanation:

I did it on prepworks

Answer 2

we are given

parent function as

`y=x^2`

(1)

vertical stretch of factor 2

so, we can multiply y-value by 2

`y=2x^2`

then a shift right of 3 units

so, we can replace x as x-3

`y=2(x-3)^2`

(2)

a shift left by 2 units

we can replace x as x+2

`y=(x+2)^2`

then a horizontal shrink factor of 1/2

so, we can multiply by 2 to x-value

`y=(2x+2)^2`

then a shift down of 5 units

we can subtract y-value by 5

so, we get

`y=(2x+2)^2-5`

(3)

a shift to the right 1 unit

we can replace x as x-1

`y=(x-1)^2`

stretched vertically by a factor of 1/2

we can multiply y-value by 1/2

`y=(1)/(2) (x-1)^2`

then is shifted down 4 units

we can subtract y-value by 4

`y=(1)/(2) (x-1)^2-4`

(4)

reflected across the x-axis

we can multiply y-value by -1

`y=-x^2`

tretched vertically by a factor of 3

multiply y-value by 3

`y=-3x^2`

shifted left 7 units

we can replace x as x+7

`y=-3(x+7)^2`