graph the function; identify the domain and range; and compare the graph with the graph of y = 1/x        y = -10/x   domain: range: compare:

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Supposing that you need to evaluate the domain and range of the function `y = -10/x` , you should remember the definitions of domain and range of a function.

The domain of function needs to contain all x values that make the function valid. The function` y = -10/x` is not valid if `x = 0` , hence, you need to reject the value x = 0 from domain. Since all x values are real numbers, then you may write the domain such that: `R - {0}.`

The range of the function is the set that contains all values of function obtained using the elements from domain, hence, the range is also `R - {0}.`

Comapring the graph `y = -10/x` to `y = 1/x` yields that the graph y = 1/x passes through two transformation: a reflection to y axis and a vertical expansion by the factor `k = -1/10` .