How do you graph #f(x)=x^2/(x+5)#?
To graph the function f(x) = x^2/(x+5), follow these steps:

Determine the domain of the function by identifying any values of x that would make the denominator (x+5) equal to zero. In this case, x cannot be 5.

Find the yintercept by substituting x=0 into the function: f(0) = 0^2/(0+5) = 0.

Determine the xintercept(s) by setting the numerator (x^2) equal to zero and solving for x. In this case, x=0 is the only xintercept.

Analyze the end behavior of the function. As x approaches positive or negative infinity, the function approaches zero.

Plot the points obtained from the yintercept, xintercept, and any additional points you choose.

Draw a smooth curve passing through the plotted points, considering the behavior of the function as x approaches 5 and infinity.
This will give you the graph of f(x) = x^2/(x+5).
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graph{x^2/(x+5) [86.4, 73.6, 45.1, 34.9]}
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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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