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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
To find the equation of y=x^3 with the given transformations, we need to consider each transformation step by step.
Step 1: Vertical Compression by a Factor of 1/7
A vertical compression by a factor of 1/7 will stretch the graph vertically. To compress the graph, we need to multiply the function by the compression factor. Therefore, the equation becomes y = (1/7)(x^3).
Step 2: Horizontal Shift 8 Units to the Left
A horizontal shift to the left indicates that the graph is moving towards negative x-values. To shift the graph 8 units to the left, we need to replace x with (x+8) in the equation. Therefore, the equation becomes y = (1/7)((x+8)^3).
Step 3: Reflection across the x-axis
A reflection across the x-axis will flip the graph upside down. To reflect the graph across the x-axis, we need to multiply the whole equation by -1. Therefore, the equation becomes y = - (1/7)((x+8)^3).
So, the equation of y=x^3 with the given transformations is y = - (1/7)((x+8)^3).