To analyze the differences between the graphs, we can look at the equations:
- Graph 1: \( y = 2 \cdot (1.2)^x \)
- Graph 2: \( y = 2 \cdot (1.2)^x + 2 \)
- Graph 3: \( y = 2 \cdot (1.2)^x - 2 \)
Difference between Graph 1 and Graph 2
- Graph 2 is obtained by taking Graph 1 and adding 2 to it.
- This means that every point on Graph 1 is shifted vertically up by 2 units to create Graph 2.
Thus, the correct selection is:
- Graph 2 is shifted two units up compared to Graph 1.
Difference between Graph 1 and Graph 3
- Graph 3 is obtained by taking Graph 1 and subtracting 2 from it.
- This means that every point on Graph 1 is shifted vertically down by 2 units to create Graph 3.
Thus, the correct selection is:
- Graph 3 is shifted two units down compared to Graph 1.
Difference between Graph 2 and Graph 3
- Graph 2 is \( 2 \cdot (1.2)^x + 2 \) and Graph 3 is \( 2 \cdot (1.2)^x - 2 \).
- The difference between the two equations is \( 2 + 2 = 4 \).
- This means that every point on Graph 3 is shifted vertically up by 4 units to reach Graph 2.
Thus, the correct selection is:
- Graph 2 is shifted four units up compared to Graph 3.
Summary of Selections
- Graph 2 is shifted two units up compared to Graph 1.
- Graph 3 is shifted two units down compared to Graph 1.
- Graph 2 is shifted four units up compared to Graph 3.