Question

Write a function based on the given parent function and the transformations in the given order.

Parent function y = x√3x3
1. Shift 9 units to the left.
2. Shift horizontally by a factor of 5.
3. Reflect across the x-axis.

Answer 1

The transformed function based on the given parent function y = x√(3x) after shifting left by 9 units, compressing horizontally by a factor of 5, and reflecting across the x-axis is y = -(x/5 + 9)√(3(x/5 + 9)).

Step-by-step explanation:

To write a function based on the given parent function y = x√(3x) and the transformations in the given order, we'll follow each transformation step by step.

Starting with the parent function, the first transformation is shifting the graph 9 units to the left, which is done by replacing x with (x + 9) in the function, giving us y = (x+9)√(3(x+9)).

Next, we horizontally compress the function by a factor of 5 by dividing the variable inside the function by 5, resulting in y = (x/5 + 9)√(3(x/5 + 9)). Lastly, we reflect the function across the x-axis, which changes the sign of the entire function to negative, hence the new function becomes y = -(x/5 + 9)√(3(x/5 + 9)).