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.

Answer 1

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.

Answer:

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)

Answer 2

 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