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