How do you graph # f(x)= x/(x+3)#?
graph{13/(x+3) [10, 10, 15, 15]}
graph{1/x [10, 10, 15, 15]}
graph{1/(x+3) [10, 10, 15, 15]}
graph{3/(x+3) [10, 10, 15, 15]}
graph{3/(x+3) [10, 10, 15, 15]}
graph{13/(x+3) [10, 10, 15, 15]}
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To graph the function f(x) = x/(x+3), follow these steps:

Determine the domain of the function, which is all real numbers except for x = 3 (since division by zero is undefined).

Find the yintercept by substituting x = 0 into the equation: f(0) = 0/(0+3) = 0/3 = 0. So, the yintercept is (0, 0).

Determine the xintercept by setting f(x) = 0 and solving for x: x/(x+3) = 0. This occurs when x = 0, so the xintercept is (0, 0).

Analyze the behavior of the function as x approaches positive and negative infinity. As x approaches infinity, f(x) approaches 1. As x approaches negative infinity, f(x) approaches 1.

Plot additional points by choosing various xvalues and calculating the corresponding yvalues using the equation.

Draw a smooth curve passing through the plotted points, considering the behavior of the function and the asymptotes.

Finally, label the x and y axes, and any other relevant points or features on the graph.
Note: The graph will have a vertical asymptote at x = 3, as the function approaches infinity as x approaches 3 from the left, and approaches negative infinity as x approaches 3 from the right.
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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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