## Question

# How to find the domain and range of a rational function?

A rational function can be represented in the form of p / q where q is not equal to 0.

## Answer: The domain of a rational number is all real numbers except those which make the denominator zero. While the range of a rational number is not as simple as the domain.

Let us proceed step by step.

Explanation:

The domain of a rational number is all real numbers except those which make the denominator zero.

While the range of a rational number is not as simple as the domain.

We need to draw the graph of the function to find the range.

For example.--

f(x) = x / (x^{2} − 4)

x^{2} − 4 = (x + 2) ( x − 2) ≠ 0

⇒ x ≠ ± 2,

### So, the domain of f is (−∞, −2) ∪ (−2, 2) ∪ (2, ∞) and the middle piece spans from −∞ to +∞, the range is (−∞,∞).

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