Question

Cubic equation that has been transformed from the parent function with a vertical compression, reflected over the y-axis and shifted up.

Answer 1

Question is incomplete

Answer:

See Explanation

Explanation:

Let the cubic function be

`f(x) = (x,y)`

First transformation: Vertical compression

Let the scale factor be a where
`0 < |a| < 1`

The new function becomes:

`f'(x) = (x,ay)`

Next: Reflection over y-axis

The rule is:
`(x,y)=>(-x,y)`

The new function becomes:

`f`

Lastly: Shifted up

Let the units up be b

The rule is:
`(x,y)=>(x,y+b)`

So, the new function becomes:

`f`

Using the rules states above, assume the cubic function is:

`f(x) = x^3`

Vertical compress
`f(x) = x^3` by
`(1)/(2)`

`f'(x) = (1)/(2)x^3`

Reflect
`f'(x) = (1)/(2)x^3` over y-axis

Rule:
`f`

Solving f'(-x)

`f'(x) = (1)/(2)x^3`

`f'(-x) = (1)/(2)(-x)^3`

`f'(-x) = -(1)/(2)x^3`

So:

`f`

Lastly: Shift
`f` by 3

Rule:
`(x,y)=>(x,y+b)`

`f'`

Solving: f"(x + 3)

`f`

Substitute x + 3 for x

`f`

So:

`f'`

`f`