Domain and range of fraction

Question

Find domain and range for 5x/(x^2-3x-4)

Answer 1

The domain of a rational function includes all real numbers except those that cause the denominator to equal zero. x² - 3x - 4 = 0 when x = -1 or x = 4, so the domain is all real numbers except -1 and 4.

Note that plugging in any x-value in the domain will give us any real number (negative, zero, positive), so the range is all real numbers.