How do you graph #y=log (x4)#?
Graph shows the vertical asymptote at x nearing 4.
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To graph ( y = \log(x  4) ), follow these steps:

Determine the domain of the function. Since the argument of the logarithm must be positive, ( x  4 > 0 ), so ( x > 4 ).

Identify any vertical asymptotes. Since the function is undefined for ( x = 4 ), there is a vertical asymptote at ( x = 4 ).

Find the xintercept by setting ( y = 0 ) and solving for ( x ). ( 0 = \log(x  4) ) implies ( x  4 = 1 ), so ( x = 5 ).

Determine the behavior of the function as ( x ) approaches positive infinity. As ( x ) approaches positive infinity, ( \log(x  4) ) approaches positive infinity.

Sketch the graph accordingly, considering the vertical asymptote at ( x = 4 ), the xintercept at ( x = 5 ), and the behavior of the function as ( x ) approaches positive infinity.
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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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