Question

What are the following transformations for the function f(x)?

f(x+2)
Reflection over the y-axis and 2 units to the left
Reflection over the x-axis and 2 units to the left
Reflection over the x-axis and 2 units to the right
Reflection over the y-axis and 2 units to the right
Which of the following describes the correct order of these transformations?

A) f(x+2), Reflection over the y-axis and 2 units to the left, Reflection over the x-axis and 2 units to the left, Reflection over the x-axis and 2 units to the right, Reflection over the y-axis and 2 units to the right
B) Reflection over the y-axis and 2 units to the left, f(x+2), Reflection over the x-axis and 2 units to the left, Reflection over the x-axis and 2 units to the right, Reflection over the y-axis and 2 units to the right
C) Reflection over the x-axis and 2 units to the left, Reflection over the x-axis and 2 units to the right, f(x+2), Reflection over the y-axis and 2 units to the left, Reflection over the y-axis and 2 units to the right
D) Reflection over the y-axis and 2 units to the left, Reflection over the x-axis and 2 units to the left, Reflection over the x-axis and 2 units to the right, Reflection over the y-axis and 2 units to the right, f(x+2)

Answer 1

The transformation f(x+2) translates the function f(x) 2 units to the left without any reflections over the x-axis or y-axis.

Step-by-step explanation:

The question asks about the effect of transformations on the function f(x), specifically the transformation f(x+2). When we apply the transformation f(x+2), we are translating the function 2 units to the left, not reflecting it over any axis. This is because, in function notation, when we see f(x + c), we translate the function horizontally by c units in the negative x-direction and f(x - c) would translate it in the positive x-direction.

Therefore, the correct transformation for f(x+2) is not a reflection over either the x-axis or the y-axis but rather a simple horizontal translation 2 units to the left. The other transformations outlined in the question (reflection over the y-axis and reflection over the x-axis followed by translations) are separate transformations that can be applied to the function and are not directly related to f(x+2).