# How do you find the domain and range and intercepTs for #R(x) = (x^2 + x - 12)/(x^2 - 4)#?

see explanation.

The denominator of R(x) cannot be zero as this would make R(x) undefined. Evaluating the denominator to zero and solving gives the values that x cannot be.

The numerator is the only part of R ( x ) that can equal zero when y = 0

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To find the domain of R(x), we need to determine the values of x for which the function is defined. In this case, the function R(x) is defined for all real numbers except the values that make the denominator equal to zero. Thus, the domain of R(x) is all real numbers except x = 2 and x = -2.

To find the range of R(x), we need to determine the set of all possible output values. Since the function is a rational function, the range will be all real numbers except for any vertical asymptotes or holes in the graph. In this case, there are no vertical asymptotes or holes, so the range of R(x) is all real numbers.

To find the x-intercepts, we set R(x) equal to zero and solve for x. In this case, we have (x^2 + x - 12)/(x^2 - 4) = 0. By factoring the numerator and denominator, we get (x + 4)(x - 3)/(x + 2)(x - 2) = 0. Setting each factor equal to zero, we find x = -4 and x = 3 as the x-intercepts.

To find the y-intercept, we set x = 0 in the function R(x). Plugging in x = 0, we get R(0) = (0^2 + 0 - 12)/(0^2 - 4) = -12/-4 = 3. Therefore, the y-intercept is (0, 3).

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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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