Answer:
In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.
Step-by-step explanation:
Let be [tex]g(x) = x^{3}[/tex] the parent function, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation, that is:
[tex]f(x) = g(x-a)-b,\,a,b\in\mathbb{R}[/tex] (1)
If [tex]a > 0[/tex], then translation is rightwards.
If [tex]b > 0[/tex], then translation in downwars.
If [tex]a = 2[/tex] and [tex]b = 1[/tex], then the resulting function is:
[tex]f(x) = g(x-2)-1[/tex]
[tex]f(x) = (x-2)^{3}-1[/tex] (2)
In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.
