Question

Question If the graph of the equation y=3x is reflected in the x-axis, the equation of the reflection is (1 point)
y=−(3^x)
y=x^3
y=3^-x
y=logx3

Answer 1

To find the equation of the reflection of \( y = 3x \) in the x-axis, we replace \( y \) with \( -y \). This gives us:

\[
-y = 3x
\]

To isolate \( y \), we multiply both sides by -1:

\[
y = -3x
\]

Now, let's look at the options provided:

1. \( y = - (3^x) \)
2. \( y = x^3 \)
3. \( y = 3^{-x} \)
4. \( y = \log_3 x \)

None of these options exactly matches \( y = -3x \). It's possible that there might be a misunderstanding. However, based on the process, the correct reflection of the line \( y = 3x \) across the x-axis is \( y = -3x \), which does not appear in the answer options.

Since none of the provided options are correct based on the expected reflection of the equation \( y = 3x \), if you have to select one from the options, please clarify or double-check the context of the question or the options provided.