Question

Question 10
1 pts
Suppose that g(x) = f(x - 2) + 7. Which
statement best compares the graph of g(x) with the graph of f(x)?
O The graph of g(x) is the graph of f(x) shifted 2 units to the left and 7 units down.
• The graph of g(x) is the graph of f(x) shifted 2 units to the right and 7 units up.
• The graph of g(x) is the graph of f(x) shifted
2 units to the left and 7 units up.
• The graph of g(x) is the graph of f(x) shifted 2 units to the right and 7 units down.

Answer 1

To analyze the transformation of the function \( g(x) = f(x - 2) + 7 \), we can break it down into two parts:

1. **Horizontal Shift**: The term \( x - 2 \) indicates a horizontal shift. Since it is \( x - 2 \), this signifies that the graph of \( f(x) \) is shifted **2 units to the right**.

2. **Vertical Shift**: The addition of \( +7 \) signifies a vertical shift. This means the graph is moved **7 units up**.

Combining these transformations, we can conclude that:

- The graph of \( g(x) \) is the graph of \( f(x) \) shifted 2 units to the right and 7 units up.

Therefore, the correct statement is:

**The graph of g(x) is the graph of f(x) shifted 2 units to the right and 7 units up.**