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 = 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