Question

What will happen to the given function if a graph is shifted 2 units left and 3 units up?(2 points) f(x)=x^3 will become g(x)= ( x+?)^3 +?

Answer 1

To shift the graph of the function \( f(x) = x^3 \) 2 units to the left and 3 units up, we need to adjust the function accordingly.

1. **Shifting left by 2 units:** To shift a function to the left by \( h \) units, we replace \( x \) with \( x + h \). Here, \( h = 2 \), so we replace \( x \) with \( x + 2 \):
\[
f(x) = (x + 2)^3
\]

2. **Shifting up by 3 units:** To shift a function up by \( k \) units, we add \( k \) to the entire function. Here, \( k = 3 \), so we add 3 to the function:
\[
g(x) = (x + 2)^3 + 3
\]

Putting it all together, the function \( g(x) \) becomes:
\[
g(x) = (x + 2)^3 + 3
\]

Thus, in the form \( g(x) = (x + ?)^3 + ? \), we have:
- The first question mark (for the left shift) is **2**.
- The second question mark (for the upward shift) is **3**.

Final answer:
\[
g(x) = (x + 2)^3 + 3
\] (where \( ? = 2 \) and \( ? = 3 \)).