Question

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x – 1)3 + 2. Which is the graph of g(x), the translated function?

Answer 1

Please, Moody, use " ^ " to denote exponentiation:

f(x) = x^3 and  g(x) = (x – 1)^3 + 2

Once you have drawn the graph of f(x) = x^3, you get the graph of g(x) by translating the entire graph of f(x) one unit to the right and then translating the result graph 2 units UP.

Answer 2

Given: $f(x)=x^3$

Translated function:

$g(x)=(x-1)^3+2$

For horizontal shift by a unit

$g(x)=f(x+a)$

If a>0 then shift left

If a<0 then shift right

For vertical shift by a unit

$g(x)=f(x)+a$

If a>0 then shift a unit up

If a<0 then shift a unit down

Shift 1 unit right

$x^3\rightarrow (x-1)^3$

Shift 2 unit up

$(x-1)^3\rightarrow (x-1)^3+2$

$f(x)\rightarrow g(x)$

Please see the attachment for graph.

Hence, we get g(x) by 1 unit right and 2 unit up translation.