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Describe the transformation of the equation y=3(2)x−1+4 compared to its parent function.
(i.e. Describe the shift left/right, up/down, stretch/compression)
1. The parent function for the equation y = 3(2)^x is a basic exponential function with a base of 2.
2. The equation y = 3(2)^x - 1 + 4 is obtained by adding the terms -1 and +4 to the parent function.
- The term -1 shifts the graph 1 unit down.
- The term +4 shifts the graph 4 units up.
3. Overall, the transformation of the equation y = 3(2)^x - 1 + 4 compared to its parent function includes:
- A vertical shift of 4 units up
- A vertical shift of 1 unit down
- No horizontal shift
- No stretch or compression
Therefore, the final transformation can be described as a vertical shift 4 units up and a vertical shift 1 unit down from the parent function y = 3(2)^x.