V(r)= 4/3r^3

Question

Do these transformations:
Horizontal shift to the right 2 units
Vertical dilation of 3
Vertical shift up 1 unit

Answer 1

To perform these transformations on the function V(r) = 4/3r^3:

1. Horizontal shift to the right 2 units:
We need to replace r with (r - 2) to achieve a horizontal shift to the right by 2 units.
V(r) = 4/3(r - 2)^3

2. Vertical dilation of 3:
We need to multiply the entire function by 3 to achieve a vertical dilation of 3.
V(r) = 3 * 4/3(r - 2)^3
Simplifying,
V(r) = 4(r - 2)^3

3. Vertical shift up 1 unit:
We need to add 1 to the function to achieve a vertical shift up by 1 unit.
V(r) = 4(r - 2)^3 + 1

Therefore, the transformed function is V(r) = 4(r - 2)^3 + 1.