Distinct Range Count
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)?$
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$