How do you graph #f(x)=(x2) / (x+2)#?
Just to run through some general points:
What is f(x) when x = 0?
Thus our first point on the graph is (0,1).
What is x at 1?
Thus our second point on the graph is (1, 1/3).
We continue in this manner until you have enough points on the graph.
graph{(x2)/(x+2) [10, 10, 5, 5]}
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To graph the function f(x) = (x2) / (x+2), follow these steps:

Determine the vertical asymptotes by setting the denominator equal to zero and solving for x. In this case, x+2 = 0, so x = 2 is a vertical asymptote.

Determine the horizontal asymptote by comparing the degrees of the numerator and denominator. Since both have a degree of 1, the horizontal asymptote is y = 1.

Find the xintercept by setting the numerator equal to zero and solving for x. In this case, x2 = 0, so x = 2 is the xintercept.

Determine the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity, f(x) approaches the horizontal asymptote y = 1. As x approaches negative infinity, f(x) also approaches y = 1.

Plot the vertical asymptote at x = 2, the horizontal asymptote at y = 1, and the xintercept at x = 2.

Choose additional xvalues to evaluate the function and plot corresponding points on the graph.

Connect the plotted points smoothly, avoiding the vertical asymptote.
The resulting graph should show a vertical asymptote at x = 2, a horizontal asymptote at y = 1, an xintercept at x = 2, and the curve of the function passing through the plotted points.
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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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