Question

Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units down on the parent function f(x)=x^3

Answer 1

Answer: Option b.

Step-by-step explanation:

 1. You have the following parent function given in the problem above:

f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)

2. If you take the parent function and make y=f(x+3), then you have:

$y=f(x+3)=(x+3)^{3}$ (The function is shifted 3 units left on the x-axis).

3. Then you if you make y=f(x+3)-2, as following, you obtain:

$y=f(x+3)-2=(x+3)^{3}-2$  (The function is shifted 2 units down on the y-axis).

4. Therefore, that is how you obtain the final function.

The answer is the graph shown in the option b.