How do you graph #f(x)= (x^3+1)/(x^2-4)#?
Graph of
graph{(x^3+1)/(x^2-4) [-40, 40, -20,20]}
Better, combine with a sign table, and/or make a variation table of f(x). (depending on your level)
Then we will be able to draw the graph, when :
N.B : J'ai hésité à te répondre en français, mais comme nous sommes sur un site anglophone, je prefère rester dans la langue de Shakespeare ;) Si tu as une question n'hésite pas!
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To graph the function f(x) = (x^3 + 1)/(x^2 - 4), follow these steps:
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Determine the domain of the function by finding the values of x for which the denominator (x^2 - 4) is equal to zero. In this case, x cannot be equal to 2 or -2, as it would make the denominator zero.
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Identify any vertical asymptotes by finding the values of x that make the denominator zero. In this case, x = 2 and x = -2 are vertical asymptotes.
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Determine any horizontal asymptotes by analyzing the degrees of the numerator and denominator. Since the degree of the numerator (3) is greater than the degree of the denominator (2), there is no horizontal asymptote.
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Find the x-intercepts by setting the numerator (x^3 + 1) equal to zero and solving for x. In this case, there are no x-intercepts.
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Find the y-intercept by substituting x = 0 into the function. In this case, the y-intercept is (0, 0.25).
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Plot additional points by selecting various x-values and calculating the corresponding y-values using the function.
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Draw the graph, connecting the plotted points and taking into account the vertical asymptotes.
Note: It may be helpful to use a graphing calculator or software to visualize the graph accurately.
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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.
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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