Question

What is the equation of the cubic function that is reflected over the x-axis, shifted c units to the left, b units down, and has a horizontal shrink by 1/3?

A. y = -1/3(x + c)^3 - b
B. y = (1/3x - c)^3 + b
C. y = -1/3(x - c)^3 - b
D. y = 1/3(x + c)^3 - b

Answer 1

The equation of the cubic function that is reflected over the x-axis, shifted c units to the left, b units down, and has a horizontal shrink by 1/3 is y = -1/3(x + c)^3 - b.

Step-by-step explanation:

The equation of the cubic function that is reflected over the x-axis, shifted c units to the left, b units down, and has a horizontal shrink by 1/3 is y = -1/3(x + c)^3 - b.

To reflect the function over the x-axis, we need a negative sign in front of the equation. To shift the function c units to the left, we subtract c inside the parentheses.

To shift it b units down, we subtract b outside the parentheses.

Finally, to achieve the horizontal shrink by 1/3, we divide x by 1/3, which is the same as multiplying x by 3.

Combining all these transformations, we get y = -1/3(x + c)^3 - b.