Note: 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=x^3 with the given transformations? vertical compression by a factor of 1/5 , horizontal shift 7 units to the left, reflection across the x-axis
Starting with the equation y = x^3, we can apply the given transformations step by step:
1. Vertical compression by a factor of 1/5: This means that every y-coordinate of the original graph will be multiplied by 1/5. So, the equation becomes y = (1/5)x^3.
2. Horizontal shift 7 units to the left: This means that we replace x with (x + 7) in the equation. So, the equation becomes y = (1/5)(x + 7)^3.
3. Reflection across the x-axis: This means that we need to multiply the entire equation by -1. So, the equation becomes y = - (1/5)(x + 7)^3.
Therefore, the equation of the transformed graph is y = - (1/5)(x + 7)^3.