+1245 Suppose the function f(x) is defined explicitly by the table \(\begin{array}{c || c | c | c | c | c} x & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & 0 & 0 & 1 & 3 & 6 \end{array}\) 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)?
+129852 OK....
The integers in the domain of f(x) are 0, 1, 2, 3, 4
So
g(0) = f(0) - 0 = 0 - 0 = 0
g(1) = f(1) - 1 = 0 - 1 = -1
g(2) = f(2) - 2 = 1 - 2 = -1
g(3) = f(3) - 3 = 3 - 3 = 0
g(4) = f(4) - 4 = 6 - 4 = 2
So...the distinct numbers in the range of g(x) are { -1, 0, 2 } ⇒ i.e., three values
