How do you graph the rational function #f(x)=6/(x^2+x2)#?
graph{6/(x^2+x2) [10, 10, 5, 5]}
hope it helps
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To graph the rational function f(x) = 6/(x^2 + x  2), follow these steps:

Determine the domain of the function by finding the values of x for which the denominator (x^2 + x  2) is equal to zero. In this case, the denominator factors as (x + 2)(x  1), so the function is undefined at x = 2 and x = 1. Therefore, the domain is all real numbers except 2 and 1.

Find the xintercepts by setting the numerator (6) equal to zero. Since the numerator is a constant, there are no xintercepts.

Find the yintercept by evaluating the function at x = 0. Substituting x = 0 into f(x), we get f(0) = 6/(0^2 + 0  2) = 6/(2) = 3. So, the yintercept is (0, 3).

Determine the vertical asymptotes by finding the values of x for which the denominator is equal to zero. In this case, the vertical asymptotes occur at x = 2 and x = 1.

Determine the horizontal asymptote by comparing the degrees of the numerator and denominator. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

Plot the xintercepts, yintercept, vertical asymptotes, and horizontal asymptote on the coordinate plane.

To complete the graph, choose additional xvalues within the domain and evaluate f(x) to find corresponding yvalues. Plot these points and connect them smoothly to create the graph.
Note: It may be helpful to use a graphing calculator or software to visualize the graph accurately.
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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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