Question

If $f(x)= \begin{cases}1, & \text { if } x \leq 0 \\ 2, & \text { if } x>0\end{cases}$
Then the values of the function at points $-0.001$ and $0.01$ are

• A. 0,1
• B. 2,1
• C. 1,2
• D. None of these

Answer 1

Answer: (C)

$f(x)=\begin{cases} 1, \text { if } x \leq 0 \\ 2, \text { if } x>0\end{cases}$
This function is of course defined at every point of the real line. Graph of this function is shown in figure. One can deduce from the graph that the value of the function at nearby points on $X$-axis remain close to each other except at $x=0$. At the points near and to the left of 0 , i.e., at points like $-0.1,-0.01,-0.001$, the value of the function is 1 . At the points near and to the right of 0 , i.e., at points like $0.1,0.01$, $0.001$, the value of the function is 2 .