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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)
Steps:
1. Start with the basic exponential function y=2^x
2. Apply a vertical stretch/compression by a factor of 3: y=3(2^x)
3. Apply a horizontal shift to the right by 1 unit: y=3(2^(x-1))
4. Apply a vertical shift up by 4 units: y=3(2^(x-1)) + 4
Description of transformation:
- The equation y=3(2)^x-1+4 is a transformation of the parent function y=2^x.
- The parent function y=2^x has a horizontal asymptote at y=0 and passes through the point (0,1).
- In the transformed function y=3(2)^x-1+4, the vertical stretch by a factor of 3 causes the exponential curve to increase more rapidly as compared to the parent function.
- The horizontal shift to the right by 1 unit shifts the entire curve to the right, causing the graph to intersect the y-axis at x=1.
- The vertical shift up by 4 units shifts the entire graph upwards, raising the horizontal asymptote to y=4.