Question

How do you translate the graph of f(x) = x3 left 4 units and down 2 units? Identify the equation of the graph.

Answer 1

f(x) = (x + 4)³ - 2

Explanation:

∵ f(x) = x³

∵ The function translated 4 units to the left

∴ The x-coordinate must added by 4 to be x + 4

∵ The function translated 2 units down

∴ The y-coordinate must be subtracted by 2 to be y - 2

∴ f(x) = (x + 4)³ - 2

Answer 2

Answer:
`f(x)=(x+4)^(3)-2`

Explanation:

You have the parent function:

`f(x)=x^(3)`

If you make f(x+4) you obtain;

`f(x+4)=(x+4)^(3)` The function is translated to the left 4 units.

If you make f(x+4)-2 you obtain;

`f(x+4)-2=(x+4)^(3)-2` Then the function is translated to the left 4 units and shifted down 2 units.

Therefore, the answer is
`f(x)=(x+4)^(3)-2`