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What is the equation of y=x3
=
3
with the given transformations?
vertical compression by a factor of 17
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. Vertical compression by a factor of 17:
To vertically compress the graph by a factor of 17, we multiply the function by 1/17. Therefore, the new equation becomes y = (1/17)x^3.
2. Horizontal shift 8 units to the left:
To shift the graph 8 units to the left, we subtract 8 from x. The equation after the horizontal shift becomes y = (1/17)(x+8)^3.
3. Reflection across the x-axis:
To reflect the graph across the x-axis, we negate the y-value. Therefore, the final equation is y = -(1/17)(x+8)^3.
The equation of y=x^3 with the given transformations is y = -(1/17)(x+8)^3.