Question

Sketch the graph of the function f(x) = -(x-4)^3 by indicating how a more basic function has been shifted, reflected, stretched, or compressed. Label all intercepts on the graph and state the end behavior

Answer 1

Explanation:

In the attached images we can see the rigid transformation of the function
`f(x) =x^(3)`

1. The basic graph
`f(x) =x^(3)`

2. The reflected graph
`f(x) = -x^(3)`

3. The displaced graph
`f(x) = -(x-4)^(3)`

Reflection: In the expression
`f(x) = -(x-4)^(3)` , 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
`f(x) = -(x-4)^(3)` and analyze the value -4, where, the sign - indicates displacement to the right and the value 4 indicates the amount that the graph shifted .