# How do you find the domain and range of #f(x)=(12x)/(x^2-36)#?

Below

But what asymptotes actually tell you about the graph is that its end points will approach the horizontal and vertical asymptotes, but they will never actually touch them. In other words, asymptotes describe the graph's shape, which can help you identify the graph's domain and range.

The graph is shown below.

graph{(12x)/(x^2-36) [-10, 10, 5, 5, 10]}

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The domain is

Consequently,

To determine the range, let

Consequently,

Consequently,

graph{12x/(x^2-36)[-16.24, 16.25, 32.49, 32.46]}

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To find the domain of the function ( f(x) = \frac{12x}{x^2 - 36} ), we need to identify any values of ( x ) that would make the denominator equal to zero. In this case, the denominator is ( x^2 - 36 ), so we set it equal to zero and solve for ( x ). The solutions are ( x = -6 ) and ( x = 6 ). Therefore, the domain of the function is all real numbers except ( x = -6 ) and ( x = 6 ).

To find the range of the function, we consider the behavior of the function as ( x ) approaches positive or negative infinity. As ( x ) approaches positive or negative infinity, the function approaches zero. Therefore, the range of the function is all real numbers except zero.

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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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