What is the domain and range of (x-1)/(x-4)?

1 Answer
Stefan V. ยท dani83
Aug 29, 2015

Domain: (-oo, 4) uu (4, + oo)
Range: (-oo, 1) uu (1, + oo)

Explanation:

The domain of the function will include all possible value of x except the value that makes the denominator equal to zero. More specifically, x=4 will be excluded from the domain, which will thus be (-oo, 4) uu (4, + oo).

To determine the range of the function, you can do a little algebraic manipulation to rewrite the function as

y = ((x - 4) + 3)/(x-4) = 1 + 3/(x-4)

Since the fraction 3/(x-4) can never be equal to zero, the function can never take the value

y = 1 + 0 = 1

This means that the range of the function will be (-oo, 1) uu (1, + oo).

graph{(x-1)/(x-4) [-18.8, 21.75, -10.3, 9.98]}

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