Question Find the basic function $r(x) = (x+7)^3$ is derived from, and how it has been transformed.

Studdy Solution

STEP 1

Assumptions
1. The function $r(x)$ is given as $(x+7)^3$ .
2. We need to identify the basic function that has been transformed to obtain $r(x)$ .

STEP 2

The basic function that has been transformed is the cubic function $f(x) = x^3$ . This is the parent function before any shifts, reflections, stretches, or compressions are applied.

STEP 3

The transformation that has been applied to the basic function $f(x) = x^3$ to obtain $r(x)$ involves a horizontal shift to the left by 7 units. This is indicated by the term $(x+7)$ inside the cubic function.

STEP 4

There are no other transformations such as reflections, vertical or horizontal stretches, or compressions indicated in the function $r(x) = (x+7)^3$ . Therefore, the only transformation is the horizontal shift.
The basic function is $f(x) = x^3$ and it has been shifted horizontally to the left by 7 units to obtain $r(x) = (x+7)^3$ .

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