# How do you find the domain and range of #f(x)=(x+7)/(x^2-49)#?

The domain is

The range is

Let's make the function simpler.

Consequently,

Consequently,

graph{(1/(x-7)) [-10.06, 10.22, 27.2, -13.34]}

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To find the domain, identify values of x that make the denominator nonzero. The domain is all real numbers except x ≠ ±7.

To find the range, analyze the behavior of the function as x approaches positive and negative infinity. The range is all real numbers except y ≠ 0.

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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.

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