Question

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

Answer 1

To shift the function \( f(x) = (x + 1)^3 \) to the left by 3 units, we need to replace \( x \) with \( x + 3 \). This leads to the following transformation:

\[
f(x) = ((x + 3) + 1)^3
\]

Simplifying this gives:

\[
f(x) = (x + 4)^3
\]

So, the equation describing the shifted function is:

\[
f(x) = (x + 4)^3 + 0
\]

Thus, the final result is:

\[
f(x) = (x + 4)^3 + 0
\]

To fill in the blanks:

\[
f(x) = (x + 4)^3 + 0
\]

So, the answer is \( f(x) = (x + 4)^3 + 0 \).