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 involves a horizontal shift to the right by 1 unit, a vertical shift upwards by 4 units, and a vertical stretch by a factor of 3.
- Horizontal shift right by 1 unit: The -1 in the exponent term (2)^x-1 causes the graph to shift to the right by one unit, compared to the parent function y=2^x.
- Vertical shift up by 4 units: The +4 at the end of the equation y=3(2)^x−1 +4 causes the graph to shift vertically upwards by 4 units, compared to the parent function.
- Vertical stretch by a factor of 3: The coefficient 3 multiplied by the entire expression 2^x in the equation y=3(2)^x−1 +4 stretches the graph vertically by a factor of 3 compared to the parent function.
In summary, the transformation of the equation y=3(2)^x−1 +4 compared to its parent function includes a horizontal shift to the right by 1 unit, a vertical shift upwards by 4 units, and a vertical stretch by a factor of 3.