Consider the two real‐valued functions f(x)=∣x∣ and g(x)=sgn(x).
Answer the following questions about these functions.
a. (i) Define the modulus function and the signum function in words as accepted in the syllabus.
b. (ii) State the domain and range of f and of g.
c. (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.
d. (iv) Using the graphs or otherwise, explain why f is continuous at x=0 while g is not continuous at x=0.