Question

What is the equation after performing a horizontal shrink by a factor of 1/3, followed by a translation 2 units up, and then a reflection in the x-axis of the function F(x) = x³ 2(x)²-9?

Answer 1

To find the equation after performing a horizontal shrink by a factor of 1/3, followed by a translation 2 units up, and then a reflection in the x-axis of the function F(x) = x³ + 2x² - 9.

Step-by-step explanation:

To find the equation after performing a horizontal shrink by a factor of 1/3, followed by a translation 2 units up, and then a reflection in the x-axis of the function F(x) = x³ + 2x² - 9, we need to apply each transformation step by step.

1. Horizontal Shrink by a factor of 1/3: We divide the x-values of the original equation by 1/3, which is equivalent to multiplying them by 3. So the equation becomes F(x) = (3x)³ + 2(3x)² - 9.
2. Translation 2 units up: We simply add 2 to the y-values of the equation. So the equation becomes F(x) = (3x)³ + 2(3x)² - 7.
3. Reflection in the x-axis: We change the sign of the y-values in the equation. So the equation becomes F(x) = (3x)³ + 2(3x)² + 7.

Therefore, the final equation after all the transformations is F(x) = (3x)³ + 2(3x)² + 7.