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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)
To describe the transformation of the equation y=3(2)x−1+4 compared to its parent function, which is y=2x, we will analyze the changes step by step:
1. Stretch/Compression: The parent function y=2x has a coefficient of 2 in front of the x, which indicates that the function compresses vertically by a factor of 2. In our transformed equation y=3(2)x−1+4, we have a coefficient of 3 outside the parentheses, which indicates a vertical stretch by a factor of 3.
2. Shift left/right: The parent function y=2x has no horizontal shift, as it passes through the origin. In our transformed equation, the x inside the parentheses is increased by 1, causing the graph to shift 1 unit to the right.
3. Shift up/down: The parent function y=2x has no vertical shift, as it also passes through the origin. In our transformed equation, the constant term +4 at the end causes the graph to shift 4 units up.
Therefore, the transformation of the equation y=3(2)x−1+4 compared to its parent function y=2x can be described as a vertical stretch by a factor of 3, a shift 1 unit to the right, and a shift 4 units up.