Question

The graph of the parent function f(x) = xº is translated to form the graph of g(x) = (x + 3) ^3 - 4. The point(0, 0) on the graph

of f(x) corresponds to which point on the graph of g(x)
(3, 4)
(3,-4)
(-3, 4)
(-3,-4)

Answer 1

(-3,-4)

Explanation:

we know that

The parent function f(x) is equal to

`f(x)=x^3`

The turning point in f(x) is the point (0,0)

The function g(x) is equal to

`g(x)=(x+3)^3-4`

The turning point in g(x) is the point (-3,-4)

so

The transformation of f(x) to g(x) is

(0,0) -----> (-3,-4)

The rule of the translation is

(x,y) -----> (x-3,y-4)

The translation is 3 units at left and 4 units down