What is the equation of y=x^3 with the given transformations? vertical compression by a factor of 1/7 , horizontal shift 8 units to the left, reflection across the x-axis
The equation of the original function y = x^3 can be transformed using vertical compression, horizontal shift, and reflection as follows:
1. Vertical compression by a factor of 1/7:
The vertical compression by a factor of 1/7 can be represented as y = (1/7)x^3.
2. Horizontal shift 8 units to the left:
The horizontal shift of 8 units to the left can be represented as y = (1/7)(x + 8)^3.
3. Reflection across the x-axis:
The reflection across the x-axis changes the sign of the function, so the equation becomes y = -(1/7)(x + 8)^3.
Therefore, the final equation after applying these transformations to y = x^3 is:
y = -(1/7)(x + 8)^3