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.

Question :

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.

y = (-1/7) (x+8)^3 or -1/7(x + 8)

Step-by-step explanation:

y = x^3   {compression factor places coefficient out in front of the polynomial}

y = (1/7) x^3  {horizontal shift 8 units to the left changes all x to x + 8}

y = (1/7) (x+8)^3   {Reflection across the x axis makes all y values negatives of one another}

-y = (1/7) (x+8)^3  {Now multiply by -1 to get y = f(x) form}

y = (-1/7) (x+8)^3 or -1/7(x + 8)

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