How do you graph #F(x)=ln(x3)#?
y = F(x). Use the inverse relation
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To graph ( F(x) = \ln(x  3) ), you can follow these steps:

Determine the domain of the function. Since the natural logarithm function ( \ln(x) ) is defined only for positive real numbers, in this case, ( x  3 > 0 ), so ( x > 3 ).

Find the vertical asymptote. The vertical asymptote occurs where the argument of the logarithm is zero, so set ( x  3 = 0 ), which gives ( x = 3 ).

Determine the behavior of the function as ( x ) approaches the asymptote. As ( x ) approaches 3 from the right side, ( \ln(x  3) ) goes to negative infinity, and as ( x ) becomes larger than 3, ( \ln(x  3) ) increases without bound.

Choose some points to plot. Pick a few values of ( x ) greater than 3, calculate the corresponding ( y )values using ( \ln(x  3) ), and plot these points.

Sketch the graph. Based on the behavior near the asymptote and the points you've plotted, sketch the curve. It should approach the vertical asymptote at ( x = 3 ), increase slowly at first, then more steeply as ( x ) increases.

Label the axes and any important points. Label the vertical asymptote at ( x = 3 ), and if needed, indicate the direction of the curve as it approaches the asymptote.

Your graph should resemble a logarithmic curve, approaching the vertical asymptote at ( x = 3 ) and increasing without bound as ( x ) increases.
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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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