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Multiple Choice
For the topic of graphs of the sine and cosine functions, what is the axis of symmetry for the graph of ?
A
B
C
The y-axis ()
D
The x-axis ()
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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.
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.
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.
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.
Therefore, the axis of symmetry for \( y = |x| \) is the y-axis, or \( x = 0 \).