Question:
Graphs of functions are given. Mark option
Graphs of functions are given. Mark option
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If a function’s graph is symmetric with respect to the $y$-axis, then $f(x) = f(-x)$ and it is an even function.
Updated On: Mar 23, 2026
- If f(x) = 3f(−x)
- If f(x) = f(−x)
- If f(x) = −f(−x)
- If 3f(x) = 6f(−x)
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The Correct Option is B
Solution and Explanation
From the graph, we observe that $f(x)$ is a horizontal line at $y = 2$ for all $x$.
For any $x$,
\[
f(x) = 2 \quad \text{and} \quad f(-x) = 2
\]
Thus $f(x) = f(-x)$ for all $x$.
This is the definition of an even function.
Options (1) and (4) would require different scaling between $f(x)$ and $f(-x)$, which is not the case here.
Option (3) implies $f$ is odd, which would require $f(x) = -f(-x)$, impossible for a constant nonzero function.
Hence,
\[
\boxed{f(x) = f(-x)}
\]
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