Question

Describe each graph in relation to its basic function.

Answer 1

Answer:

In a nutshell, $f(x)$ is obtained by applying an horizontal translation on $g(x)$, followed by a vertical translation.

Step-by-step explanation:

Let be $g(x) = x^{3}$ the parent function, $f(x)$ is obtained by applying an horizontal translation on $g(x)$, followed by a vertical translation, that is:

$f(x) = g(x-a)-b,\,a,b\in\mathbb{R}$ (1)

If $a > 0$, then translation is rightwards.

If $b > 0$, then translation in downwars.

If $a = 2$ and $b = 1$, then the resulting function is:

$f(x) = g(x-2)-1$

$f(x) = (x-2)^{3}-1$ (2)

In a nutshell, $f(x)$ is obtained by applying an horizontal translation on $g(x)$, followed by a vertical translation.