Final answer:
The function f(x)=-3(1/2x)³+7 contains a reflection across the x-axis, a vertical stretch by a factor of 3, a horizontal compression by a factor of 2, and a vertical shift upwards by 7 units.
Step-by-step explanation:
Description of all transformations from the parent function given the function below: f(x)=-3(1/2x)³+7
Let's break down the transformations one by one:
Negative Sign: The negative sign in front of the function indicates a reflection across the x-axis.
Vertical Stretch: The coefficient 3 is a vertical stretch by a factor of 3. Normally, a stretch might be confused with a 'Vertical Compression', but here it's actually making the graph of the function stretch away from the x-axis by a factor of 3. This means that for every point on the parent graph, its distance from the x-axis is tripled.
The horizontal compression by a factor of 2: Because of the 1/2 inside the cube function, we're compressing the graph horizontally by a factor of 2. Every point on the parent function which was at a distance 'x' from the y-axis will now be at 'x/2'.
Vertical Shift: Addition of 7 to the function denotes a vertical shift upwards by 7 units.
Starting from the parent function x³, these transformations drastically change the graph into the new function f(x).