find domain and range: h(x) = x^2 - 3x - 4 / (x - 4)?

h(x) = (x² - 3x - 4) / 9x - 4)

h(x) is a fraction and, as such, the denominator canot equal zero, so

x - 4 ≠ 0

x ≠ 4

Domain: All Real x | x ≠ 4

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Since the division of h(x) results in the rational expression x + 1, and x cannot be 4,

Range: All Real y | y ≠ 5

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We can rewrite the function as h(x) = (x - 4)(x + 1)/(x - 4)

The domain is then evidently all real numbers except x = 4 (since x = 4 makes the function indeterminate...)

The range will turn out to be all real numbers except y = 5 (since that would have been the value of the function at x = 4 if we canceled the common factor of (x - 4) in h(x))

NOTE: The point (4, 5) would appear as a "hole" in the graph of h(x)

This function creates a line with a positive slope, so it has a domain and range of all real numbers -

(-infinity, +infinity)