Question

Worth 60 pts

Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function.
y=^3√-8x-4

Answer 1

Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.

The graph is reflected over the x-axis.

The graph is also reflected over the y-axis.

The graph is vertically stretched by a factor of 2.

The graph is translated ½ unit to the left.

Explanation:

Copy all of this down, I got 100%

Answer 2

y=(-8x-4)^(1/3)
y=(x)^(1/3)
y=a*(b(x-c))^(1/3))+d
In this equation, a is equal to one and d is equal to 0, so the equation is reduced to y=(b(x-c))^(1/3). Here, you can see that the b value is equal to -8, which would leave a c value of (-1/2) according to the equation.
This would mean that the transformations from y=x^(1/3) to the equation in the problem would include:
a horizontal shift of -1/2, or to the left of the y-axis by .5 units,
a reflection across the x-axis, due to the negative b value,
and the b value of 8, ignoring the sign due to that demonstrating the reflection, would mean that it is horizontally compressed by 1/8.