Question

Write the equation that describes the function f ( x) = (x + 1)^3 shifted to the left three units f(x )= ( x + ___)^3 +____

Answer 1

To shift the function \( f(x) = (x + 1)^3 \) to the left by three units, you need to replace \( x \) with \( x + 3 \) in the function.

Here's the step-by-step transformation:

1. Start with the original function:
\[
f(x) = (x + 1)^3
\]

2. Shift to the left by 3 units by replacing \( x \) with \( x + 3 \):
\[
f(x) = ((x + 3) + 1)^3
\]

3. Simplify the expression inside the cube:
\[
f(x) = (x + 4)^3
\]

So the new function after the shift is:
\[
f(x) = (x + 4)^3
\]

In the form you provided, this is:
\[
f(x) = (x + 4)^3 + 0
\]

Thus, the values you fill in are:
\[
(x + 4)^3 + 0
\]

So, the final answer is:
\[
\text{Shifted form: } f(x) = (x + 4)^3 + 0
\]