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

Answer: $f(x)=(x+4)^{3}-2$

Step-by-step 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  $f(x)=(x+4)^{3}-2$

Answer 2

Answer:

f(x) = (x + 4)³ - 2

Step-by-step 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