Step-by-step explanation:
In the attached images we can see the rigid transformation of the function [tex]f(x) =x^{3}[/tex]
1. The basic graph [tex]f(x) =x^{3}[/tex]
2. The reflected graph [tex]f(x) = -x^{3}[/tex]
3. The displaced graph [tex]f(x) = -(x-4)^{3}[/tex]
Reflection: In the expression [tex]f(x) = -(x-4)^{3}[/tex] , the sign - before the parenthesis indicates that the function is reflected in the x axis, for this case the function is even, this means that -f(x) = f(-x)
, then the reflection on the x axis is equal to the reflection on the y axis.
Displacement: We observe the term (x-4) of the function [tex]f(x) = -(x-4)^{3}[/tex] and analyze the value -4, where, the sign - indicates displacement to the right and the value 4 indicates the amount that the graph shifted
.
