Question

Parent function: y=x³ Shift 2.7 units to the left. Reflect across the y-axis. Shift upward 5.6 units.

Answer 1

The parent function y = x³ is transformed by shifting it 2.7 units to the left, reflecting it across the y-axis, and then shifting it upward by 5.6 units, resulting in the final equation y = -(x + 2.7)³ + 5.6.

Step-by-step explanation:

The student's question involves transformations of the basic cubic function y = x³. To apply the described transformations to the parent function, we follow these steps:

1. Shift 2.7 units to the left: y = (x + 2.7)³.
2. Reflect across the y-axis: y = -(x + 2.7)³. Here, the negative sign reflects the graph across the y-axis.
3. Shift upward 5.6 units: y = -(x + 2.7)³ + 5.6. This final addition moves the graph up by 5.6 units on the y-axis.

The final transformed equation after all the described operations is y = -(x + 2.7)³ + 5.6. This transformation includes translations and reflections, which are common topics in algebra and precalculus courses. By understanding these transformations, students can manipulate a wide variety of functions to fit specific criteria or graphical representations.