jmc

Question

Suppose the function f(x) is defined explicitly by the table arrayc || c | c | c | c | c x & 0 & 1 & 2 & 3 & 4 f(x) & 0 & 0 & 1 & 3 & 6 array This function is defined only for the values of x listed in the table. Suppose g(x) is defined as f(x)-x for all numbers x in the domain of f. How many distinct numbers are in the range of g(x)?

Accepted Answer

We can extend our table to include g(x): arrayc || c | c | c | c | c x & 0 & 1 & 2 & 3 & 4 f(x) & 0 & 0 & 1 & 3 & 6 g(x) & 0 & -1 & -1 & 0 & 2 array As the table clearly shows, g(x) takes three distinct values: 0, -1, and 2. Thus, the range of g(x) contains 3 numbers.