MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Consider the two real‐valued functions f(x)=∣x∣ and g(x)=sgn(x).
Answer the following questions about these functions.
(i) Define the modulus function and the signum function in words as accepted in the syllabus.
(ii) State the domain and range of f and of g.
(iii) Draw rough sketches of the graphs of y=f(x) and y=g(x) on the same set of axes, clearly labelling all intercepts and key points.
(iv) Using the graphs or otherwise, explain why f is continuous at x=0 while g is not continuous at x=0.