Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the equation of y=x3 with the given transformations? vertical compression by a factor of 15 , horizontal shift 7 units to the left, reflection across the x-axis
Given the equation y = x^3, we can apply the given transformations one by one.
First, let's apply the vertical compression by a factor of 15. To compress vertically, we need to multiply the equation by the compression factor. Therefore, the equation becomes y = 15x^3.
Next, we apply the horizontal shift 7 units to the left. To shift horizontally, we need to add the shift value to the x-coordinate. So the equation becomes y = 15(x + 7)^3.
Finally, we apply the reflection across the x-axis. To reflect across the x-axis, we need to multiply the equation by -1. Therefore, the final equation is y = -15(x + 7)^3.