Question

The function g(x)=f(x+3)+2. Which of the following is true
Shifted 3 units right and 2 units above the graph if f(x)
Shifted 3 units to left and 2 units above the graph f(x)
Shifted 3 units to right and 2 units below f(x)
Shifted 3 units to left and 2 units below f(x)

Answer 1

To analyze the function \( g(x) = f(x+3) + 2 \), we can look at how it transforms the original function \( f(x) \).

1. The term \( (x + 3) \) indicates a horizontal shift. The function \( f(x + 3) \) means the graph of \( f(x) \) is shifted to the **left** by 3 units. (When you see \( x + c \) in the argument of a function, it shifts the graph left by \( c \) units.)

2. The \( + 2 \) outside the function indicates a vertical shift. The function \( f(x) + 2 \) means the graph of \( f(x) \) is shifted **upward** by 2 units.

Putting both shifts together, the graph of \( f(x) \) is shifted:
- **3 units to the left** (due to \( x + 3 \))
- **2 units up** (due to +2)

Thus, the correct statement is:

**Shifted 3 units to left and 2 units above the graph of \( f(x) \).**