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What is the equation of y=x3
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 apply each transformation step by step.
1. Start with the original function y = x^3.
2. Apply the vertical compression by a factor of 1/7:
y = (1/7)x^3
3. Apply the horizontal shift 8 units to the left:
To shift 8 units to the left, we replace x with (x + 8):
y = (1/7)(x + 8)^3
4. Apply the reflection across the x-axis:
To reflect across the x-axis, we negate the entire function:
y = -(1/7)(x + 8)^3
Therefore, 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) is:
y = -(1/7)(x + 8)^3