Question

cube and cube root functions and equations
the graph of the parent function $f(x)=x^3$ is transformed 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 $g(x)$?
$(3, 4)$
$(-3,-4)$
$(3,-4)$
$(-3, 4)$

Explanation:

Step1: Identify horizontal shift

For $g(x)=(x+4)^3 - 4$, compared to $f(x)=x^3$, the horizontal shift is given by $x \to x + 4$, which means shift left by 4 units. To find the new $x$-coordinate from $(1,0)$:
$1 - 4 = -3$

Step2: Identify vertical shift

The vertical shift is $-4$, meaning shift down by 4 units. To find the new $y$-coordinate from $(1,0)$:
$0 - 4 = -4$

Answer:

$(-3, -4)$