For the topic of graphs of the sine and cosine functions, what is the axis of symmetry for the graph of $y=\left|x\right|$?

• A. $y=x$
• B. $x=1$
• C. The y-axis ($x=0$)
• D. The x-axis ($y=0$)

Answer: (C)

Verified step by step guidance

1. Identify the function given: \( y = |x| \). This is the absolute value function, which is not a sine or cosine function but is often discussed in relation to symmetry and graphs.
2. Recall that the absolute value function outputs the distance of \( x \) from zero on the number line, so it is always non-negative and 'mirrors' values on the negative side of the x-axis to the positive side.
3. To find the axis of symmetry, consider the line about which the graph is mirrored. For \( y = |x| \), the graph is symmetric about the vertical line \( x = 0 \), which is the y-axis.
4. Check the other options: \( y = x \) is a line with slope 1, not an axis of symmetry; \( x = 1 \) is a vertical line but not the axis of symmetry for \( y = |x| \); \( y = 0 \) is the x-axis, which is not the axis of symmetry here because the graph is not mirrored across the x-axis.
5. Therefore, the axis of symmetry for \( y = |x| \) is the y-axis, or \( x = 0 \).