Question

What transformation of the graph of y = sin x results in the graph of y = sin (-0)?

A. Vertical shift 1 unit down
B. Vertical shift 1 unit up
C. Reflection over the y-axis
D. Reflection over the x-axis

Answer 1

Let's analyze the transformation needed to go from the function \( y = \sin x \) to \( y = \sin(-0) \).

First, note that \( \sin(-0) \) is just \( \sin(0) \). Therefore, \( y = \sin(-0) \) is essentially \( y = 0 \).

The sine function is odd, which means \( \sin(-x) = -\sin(x) \). Thus, transforming \( y = \sin x \) into \( y = \sin(-x) \) involves reflecting the graph over the y-axis. However, since \( \sin(-0) \) leads to a constant function, \( y = 0 \), this results in shifting the graph down to the x-axis.

None of the options directly indicate the transition based on expressing \( \sin(-0) \), but we could infer a transformation based on the sine values.

The transformation that most closely aligns with this understanding in terms of graph behavior from \( y = \sin x \) to \( y = 0 \) is:

**C. Reflection over the y-axis.**

This is because the reflection would technically keep the sine function's amplitude and period, but in terms of horizontal placement when considering negative inputs, it's primarily about how the sign of the value changes.

However, if we need to consider the output value translations, the sine function becomes 0 at both \( x = 0 \) and \( x = \pm \pi \), hinting at broader transformation concepts.

Thus, it is safe to conclude that:

**Answer: C. Reflection over the y-axis.**