Consider the function f(x) = { (1-x, x<0)(1, x=0)(1+x, x>0)

Question

Consider the function

\(f(x) =\)\(\begin{cases} 1-x,& \quad x<0\\ 1,& \quad x=0\\ 1+x ,& \quad x>0 \end{cases} \)

(i) Complete the following table

x	-2	-1	0	1	2
f(x)	.......	.......	.......	......	......

(ii) Draw a rough sketch of f (x).

(iii) What is your inference from the graph about Its continuity. Verify your answer using limits.

Answer 1

(i) 

x	-2	-1	0	1	2
f(x)	3	2	1	2	3

 Since, f (- 2) = 1 – (- 2) = 3, f (-1) = 1 – (-1) = 2,
f(1) = 1 + (1) = 2, f (2) = 1 + (2) = 3.

(ii)

(iii) From the graph we can see that there is no break or jump at x = 0. Therefore continuous.
From the figure we can see that
f(0^–) = 1 f(0⁺) = 1 and f(0) = 1
Hence, f(0^–) = f(0⁺) = f(0) = 1.
Therefore continuous.