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If f(x) is an even function, then the graph y = f(x) will be symmetrical about
- a)x-axis
- b)y-axis
- c)Both the axes
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If f(x) is an even function, then the graph y = f(x) will be symmetric...
y — axis by definition.
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If f(x) is an even function, then the graph y = f(x) will be symmetric...
Symmetry of Graphs of Even Functions
Definition of an Even Function: An even function is a function f(x) such that f(-x) = f(x) for all x in the domain of f.
Explanation of Even Functions: This means that the function is symmetrical about the y-axis. When you replace x with -x, the function value does not change. In other words, if you reflect the graph of an even function across the y-axis, you get the same graph.
Example of an Even Function: An example of an even function is y = x^2. When you replace x with -x, you get y = (-x)^2 = x^2. The graph of y = x^2 is a parabola that is symmetrical about the y-axis.
Answer: Therefore, if f(x) is an even function, then the graph y = f(x) will be symmetrical about the y-axis. This means that if you reflect the graph across the y-axis, you get the same graph. The correct answer is option B.
Definition of an Even Function: An even function is a function f(x) such that f(-x) = f(x) for all x in the domain of f.
Explanation of Even Functions: This means that the function is symmetrical about the y-axis. When you replace x with -x, the function value does not change. In other words, if you reflect the graph of an even function across the y-axis, you get the same graph.
Example of an Even Function: An example of an even function is y = x^2. When you replace x with -x, you get y = (-x)^2 = x^2. The graph of y = x^2 is a parabola that is symmetrical about the y-axis.
Answer: Therefore, if f(x) is an even function, then the graph y = f(x) will be symmetrical about the y-axis. This means that if you reflect the graph across the y-axis, you get the same graph. The correct answer is option B.
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