Question

The graph of the parent function f(x) = x is translated to form the graph of g(x) = (x + 5)3 - 6. The point (0,0) on the graph

of f(x) corresponds to which point on the graph of g(x)?
O (5, -6)
(-5, -6)
(5,6)
(-5,6)

Answer 1

(-5, -6)

Explanation:

The correct question is

The graph of the parent function f(x)=x^3 is translated to from the graph of g(x)=(x+5)^3-6. The point (0,0) on the graph of f(x) corresponds to which point on the graph of g(x)?

see the attached figure to better understand the problem

we have that

`f(x)=x^(3)`

`g(x)=(x+5)^3-6`

we know that

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

The turning point in the function g(x) is (-5,-6)

so

The translation has the following rule

(0,0) -----> (-5,-6)

(x,y) ----> (x-5,y-6)

The translation is 5 units at left and 6 units down

therefore

The point (0,0) on the graph of f(x) corresponds to (-5,-6) on the graph of g(x)