Write a function based on the given parent function and the transformations in the given order.
-Parent function $y = \sqrt [ 3 ] { x }$
1. Shift 9 units to the left.
2. Shift horizontally by a factor of 5.
3) Reflect across the x-axis.
A) $y = - \sqrt [ 3 ] { \frac { 1 } { 5 } x + 9 }$
B) $y = - \sqrt [ 3 ] { 5 x - 9 }$
C) $y = \sqrt [ 3 ] { - \frac { 1 } { 5 } x - 9 }$
D) $y = - \sqrt [ 3 ] { 5 x + 9 }$

Question

Write a function based on the given parent function and the transformations in the given order.
-Parent function $y = \sqrt [ 3 ] { x }$ 
1. Shift 9 units to the left. 
2. Shift horizontally by a factor of 5.
3) Reflect across the x-axis. 
A) $y = - \sqrt [ 3 ] { \frac { 1 } { 5 } x + 9 }$
B) $y = - \sqrt [ 3 ] { 5 x - 9 }$
C) $y = \sqrt [ 3 ] { - \frac { 1 } { 5 } x - 9 }$
D) $y = - \sqrt [ 3 ] { 5 x + 9 }$

Quizplus · Accepted Answer

The correct transformation sequence is: 1. Shift 9 units to the left, which adds 9 inside the function, making it $y = \sqrt[3]{x + 9}$.2. Horizontal stretch by a factor of 5, which multiplies $x$ by $\frac{1}{5}$, making it $y = \sqrt[3]{\frac{1}{5}x + 9}$.3. Reflect across the x-axis, which adds a negative sign in front of the function, making it $y = -\sqrt[3]{\frac{1}{5}x + 9}$.

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