Enter your answer and show all the steps that you use to solve this problem in the space provided.%0D%0A%0D%0AWhat is the equation of y=x3%0D%0A%0D%0A=%0D%0A%0D%0A3%0D%0A with the given transformations?%0D%0A%0D%0Avertical compression by a factor of 15%0D%0A1%0D%0A5%0D%0A , horizontal shift 7 units to the left, reflection across the x-axis
To find the equation of the given function with the given transformations, we need to apply each transformation step by step.
1. Vertical Compression by a Factor of 1/5:
The equation of the function after the vertical compression is y = (1/5)x^3.
2. Horizontal Shift 7 Units to the Left:
To shift the function 7 units to the left, we subtract 7 from x. Therefore, the new equation becomes y = (1/5)(x+7)^3.
3. Reflection across the x-axis:
To reflect the function across the x-axis, we change the sign of y. Therefore, the final equation is y = -(1/5)(x+7)^3.
So, the equation of y = x^3 with the given transformations is y = -(1/5)(x+7)^3.