Question

Which function represents a vertical compression, reflection in the x-axis, and a translation down 3 units in relation to the parent function?

A) y = -2/3(x - 3)^3
B) y = -(2/3x)^2 - 3
C) y = -2/3x^2 - 3
D) y = 2/3(-x + 3)^2

Answer 1

The function that represents a vertical compression, reflection in the x-axis, and a translation down 3 units is y = -2/3x^2 - 3.

Step-by-step explanation:

The function that represents a vertical compression, reflection in the x-axis, and a translation down 3 units in relation to the parent function is option C) y = -2/3x^2 - 3.

To understand why this is the correct option, let's break it down:

1. Vertical compression: The coefficient in front of the x^2 term determines the vertical stretch or compression. In this case, the coefficient is -2/3, which indicates a vertical compression.
2. Reflection in the x-axis: The negative sign in front of the function reflects it in the x-axis.
3. Translation down 3 units: The constant term -3 represents a downward translation of 3 units.