It appears that there are some missing details in the problem statement. Specifically, we need the following information to fully understand the translation and express \( g(x) \) in terms of \( f(x) \):
1. The number of units by which the graph of \( f(x) \) is translated.
2. The direction of the translation (left, right, up, down).
Let's denote:
- \( a \) as the number of units the graph is translated horizontally.
- \( b \) as the number of units the graph is translated vertically.
- The direction of the translation.
Generally, a function translation can be described by:
- A horizontal translation by \( a \) units to the right: \( g(x) = f(x - a) \)
- A horizontal translation by \( a \) units to the left: \( g(x) = f(x + a) \)
- A vertical translation by \( b \) units upward: \( g(x) = f(x) + b \)
- A vertical translation by \( b \) units downward: \( g(x) = f(x) - b \)
For example, if the graph of \( f(x) \) is translated 3 units to the right and 2 units up, the function \( g(x) \) would be:
\[ g(x) = f(x - 3) + 2 \]
Without the specific values and directions, we can't provide the exact expression for \( g(x) \). Please provide the translation details for a complete answer.
The graph g(x) is the graph of f(x) translated units , and g(x) = .
1 answer