How do you graph #y =(x^2+4x2)/(x^2x7)#?
See graph and details.
By actual division,
See graph, with asymptotes. y = 1, x = a and x = b. graph{(y(x^2x7)(x^2+4x2))(y1)(x1/21/2sqrt29+0.00001y)(x1/2+1/2sqrt29+0.00001y)=0}
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To graph the function y = (x^2 + 4x  2)/(x^2  x  7), follow these steps:

Determine the domain of the function by finding the values of x for which the denominator (x^2  x  7) is not equal to zero. In this case, the denominator factors as (x  3)(x + 2), so the function is undefined at x = 3 and x = 2.

Find the yintercept by substituting x = 0 into the equation. y = (0^2 + 4(0)  2)/(0^2  0  7) simplifies to y = 2/(7) = 2/7.

Determine the xintercepts by setting y = 0 and solving for x. However, in this case, the numerator (x^2 + 4x  2) does not factor easily. Therefore, you can use a graphing calculator or software to find the approximate xintercepts.

Analyze the behavior of the function as x approaches positive and negative infinity. As x becomes very large or very small, the terms involving x^2 dominate the function. Therefore, the function approaches y = 1 as x approaches positive or negative infinity.

Plot the obtained points, including the yintercept and xintercepts, on a graph. Use the behavior analysis to sketch the curve between the intercepts.
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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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