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)
The transformation of the equation y=3(2)^x−1+4 compared to its parent function y=2^x is as follows:
1. Shift left/right: The equation has been shifted 1 unit to the right compared to the parent function. This is because of the "-1" inside the exponent which shifts the graph 1 unit to the right.
2. Shift up/down: The equation has been shifted 4 units up compared to the parent function. This is because of the "+4" outside the exponential term which shifts the graph 4 units up.
3. Stretch/compression: The equation has been stretched vertically by a factor of 3 compared to the parent function. This is because of the coefficient of 3 in front of the exponential term which stretches the graph vertically by a factor of 3.
Overall, the transformation of the equation y=3(2)^x−1+4 compared to its parent function y=2^x includes a shift to the right, a shift up, and a vertical stretch by a factor of 3.