# How do you graph #y=ln(x+3)#?

Examining the graph, we can see that the function ln(x) has a vertical asymptote at x=0 and an x-intercept at 1 (or in coordinate form (1,0) by nature.

It helps to refer to ln(x) when graphing ln(x+3) because, when the transformation rules are applied, each x value is translated or shifted 3 units to the left. To manually shift the x value, you take the point (1,0) and shift it 3 units to the left, making your new point (-2,0). You should also note that the vertical asymptote is now x=-2, so when you graph the function, draw your line getting closer to -2 from the left while the right keeps increasing.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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