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 up: The entire graph of y=3(2)^x has been shifted up by 4 units compared to y=2^x. This is indicated by the constant term +4 added to the equation.
2. Shift right: The graph of y=3(2)^x has been shifted 1 unit to the right compared to y=2^x. This is indicated by the -1 inside the exponent of 2.
3. Stretch/Compression: The value of 3 in front of the exponential term (2)^x indicates a vertical stretch of the graph compared to the parent function. This means that the graph of y=3(2)^x will be stretched vertically by a factor of 3.
Therefore, compared to its parent function y=2^x, the equation y=3(2)^x−1+4 has been shifted up by 4 units, shifted 1 unit to the right, and vertically stretched by a factor of 3.