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The graph of the function f : R → R defined by f(x) = |x|
- a)A line lying in first and third quadrant
- b)A straight line
- c)Symmetrical with respect to y – axis
- d)A pair of parallel lines
Correct answer is option 'C'. Can you explain this answer?
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The graph of the function f : R → R defined by f(x) = |x|a)A lin...
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Wheather we take any +ve or -ve value of x, after putting the value in f(x)=|x|, the resultant value will always be +ve. So, graph will be symmetric with respect to y-axis.
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The graph of the function f : R → R defined by f(x) = |x|a)A lin...
Graph of the function f(x) = |x|
The graph of the function f(x) = |x| is symmetrical with respect to the y-axis. This means that if you fold the graph along the y-axis, the two halves will coincide.
Explanation:
- The absolute value function |x| is defined as the distance of x from 0 on the number line.
- For positive values of x, |x| = x, and for negative values of x, |x| = -x.
- This results in a V-shaped graph with the vertex at the origin.
- Since the function is symmetric about the y-axis, both the positive and negative sides of the graph are mirror images of each other.
Conclusion:
The graph of the function f(x) = |x| is symmetrical with respect to the y-axis. This symmetry is a key characteristic of absolute value functions and can help in understanding their behavior and properties.
The graph of the function f(x) = |x| is symmetrical with respect to the y-axis. This means that if you fold the graph along the y-axis, the two halves will coincide.
Explanation:
- The absolute value function |x| is defined as the distance of x from 0 on the number line.
- For positive values of x, |x| = x, and for negative values of x, |x| = -x.
- This results in a V-shaped graph with the vertex at the origin.
- Since the function is symmetric about the y-axis, both the positive and negative sides of the graph are mirror images of each other.
Conclusion:
The graph of the function f(x) = |x| is symmetrical with respect to the y-axis. This symmetry is a key characteristic of absolute value functions and can help in understanding their behavior and properties.
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The graph of the function f : R → R defined by f(x) = |x|a)A line lying in first and third quadrantb)A straight linec)Symmetrical with respect to y – axisd)A pair of parallel linesCorrect answer is option 'C'. Can you explain this answer?
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