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

A,B,C,D... Give explanations please!

Answer 1

Let

g(x)--------> the translation of the function f(x)

we know that

the rule of the translation is

`3` units left and
`2` units down

that means

`(x,y)-------> (x-3,y-2)`

so

In the function f(x) the point
`(0,0)` is equal at the point
`(-3,-2)` in the function g(x)

therefore

the function g(x) is equal to

`g(x)=f(x+3)-2`

`g(x)=(x+3)^(3) -2`

The answer is

a) the rule of the translation is
`(x,y)-------> (x-3,y-2)`

b) The graph in the attached figure