Write a function based on the given parent function and the transformations in the given order.
-Parent function: $y = x ^ { 3 }$
1. Shift 6.8 units to the right.
2. Reflect across the y-axis.
3. Shift downward 5.2 units.
A) $y = ( - x + 6.8 ) ^ { 3 } + 5.2$
B) $y = - ( x + 6.8 ) ^ { 3 } + 5.2$
C) $y = ( - x - 6.8 ) ^ { 3 } - 5.2$
D) $y = - ( x - 6.8 ) ^ { 3 } - 5.2$

Question

Write a function based on the given parent function and the transformations in the given order.
-Parent function: $y = x ^ { 3 }$ 
1. Shift 6.8 units to the right. 
2. Reflect across the y-axis.
3. Shift downward 5.2 units. 
A) $y = ( - x + 6.8 ) ^ { 3 } + 5.2$
B) $y = - ( x + 6.8 ) ^ { 3 } + 5.2$
C) $y = ( - x - 6.8 ) ^ { 3 } - 5.2$
D) $y = - ( x - 6.8 ) ^ { 3 } - 5.2$

Quizplus · Accepted Answer

The correct transformations applied to the parent function $y = x^3$ in the given order are: 1. Shift 6.8 units to the right: $y = (x - 6.8)^3$.2. Reflect across the y-axis: $y = (-x - 6.8)^3$, because reflecting across the y-axis changes $x$ to $-x$, and since we already shifted to the right, it becomes $-x - 6.8$.3. Shift downward 5.2 units: $y = (-x - 6.8)^3 - 5.2$, which matches option C.

Write a Function Based on the Given Parent Function and the Transformations