Question

Which of the following transformations describe the graph of the transformed function compared with the parent function? Select all that apply.

A. Reflected over the x-axis
B. Translated 2 units left
C. Translated 2 units right
D. Compressed by a factor of 0.4
E. Stretched by a factor of 0.4
F. Translated 2 units up
G. Translated 2 units down

Answer 1

The question involves transformations of a function's graph in a coordinate system, such as reflections, translations, compressions, and stretches. Correct transformations are reflected over the x-axis, translated 2 units left/right/up/down, and compressed by a factor of 0.4, while stretched by a factor of 0.4 is usually considered a compression.

Step-by-step explanation:

The question concerns how certain transformations affect the graph of a function. When we describe transformations of functions in a coordinate system, we're referring to changes in the graph's position or shape relative to the original or parent function. To understand these changes, it's essential to know the effects of different types of transformations:

• Reflected over the x-axis: This transformation flips the graph across the x-axis, effectively inverting it vertically.
• Translated 2 units left: This means the graph is moved horizontally to the left side of the coordinate system by two units.
• Translated 2 units right: Conversely, this moves the graph horizontally to the right side of the coordinate system by two units.
• Compressed by a factor of 0.4: This transformation scales the graph downward vertically, making it narrower than the parent function.
• Stretched by a factor of 0.4: This could be an incorrect choice because stretching usually involves a factor greater than 1. A stretch by a factor of 0.4 would actually be a compression.
• Translated 2 units up: This translates the graph vertically upward in the coordinate system by two units.
• Translated 2 units down: This translates the graph vertically downward in the coordinate system by two units.

Based on the information given, selections A (Reflected over the x-axis), B (Translated 2 units left), C (Translated 2 units right), D (Compressed by a factor of 0.4), F (Translated 2 units up), and G (Translated 2 units down) describe possible transformations of a function's graph. Option E (Stretched by a factor of 0.4) does not typically refer to a stretch; it suggests a compression instead.