Show all our steps to get the answer
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 y = 2^x, we need to look at how each of the numbers outside and inside the exponential function affects the graph.
1. First, let's look at the number 3 outside the exponential function in the transformed equation. This number acts as a vertical stretch because it multiplies the entire function by 3. This means that the transformed function will be vertically stretched by a factor of 3 compared to the parent function.
2. Next, the number 2 inside the exponential function in the transformed equation also plays a role in stretching the function, but in this case, it results in a horizontal compression. The original function y = 2^x has a horizontal stretch of 1, whereas the transformed function has a horizontal compression of 1/2. This means that the graph is squeezed horizontally by a factor of 1/2.
3. The constant term -1 in the transformed equation causes a vertical shift downward by 1 unit compared to the parent function. This means that all points on the graph of the transformed function are shifted down by 1 unit.
4. Finally, the constant term +4 in the transformed equation results in a vertical shift upward by 4 units compared to the parent function. This means that all points on the graph of the transformed function are shifted up by 4 units.
In summary, the transformation of the equation y = 3(2)^x - 1 + 4 compared to its parent function y = 2^x involves a vertical stretch by a factor of 3, a horizontal compression by a factor of 1/2, a vertical shift downward by 1 unit, and a vertical shift upward by 4 units.