How do you determine if # abs (x)/ x# is an even or odd function?
x = 0 is a point of graphbreakingdiscontinuity. For x > o, y =
Answer is brief but selfexplanatory.
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so it is an odd function
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To determine if ( \frac{\left x \right}{x} ) is an even or odd function, we examine its symmetry properties with respect to the origin.

Even Function: A function ( f(x) ) is even if ( f(x) = f(x) ) for all ( x ) in its domain. In other words, if replacing ( x ) with ( x ) doesn't change the function's value. [ \frac{\left x \right}{x} = \frac{\left x \right}{x} ]

Odd Function: A function ( f(x) ) is odd if ( f(x) = f(x) ) for all ( x ) in its domain. In other words, if replacing ( x ) with ( x ) changes the sign of the function's value. [ \frac{\left x \right}{x} = \frac{\left x \right}{x} ]
Now, let's evaluate ( \frac{\left x \right}{x} ) for both cases:
When ( x ) is positive, ( \frac{\left x \right}{x} = \frac{x}{x} = 1 ). When ( x ) is negative, ( \frac{\left x \right}{x} = \frac{x}{x} = 1 ).
Since ( \frac{\left x \right}{x} ) changes sign when ( x ) changes sign, it is an odd function.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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