Spell out your first name and last name. Let m be the number of characters in your first name and n be the number of characters in your last name. (m = 4, n = 4 ) Find one function that

a) has infinitely many vertical asymptotes and infinitely many x-intercepts on the interval (-n,-n+1),

b) has infinitely many vertical asymptotes and no x-intercept on (0,m),

c) has infinitely many x-intercepts and no vertical asymptotes on (10m,100m),

d) is continuous and greater than 10^100 on [-n+1, 0], and

e) is continuous and less than -100! on [m,10m]

You must express the function and all its zeros and asymptotes algebraically.

What software or technology would you use to graph such a function? Explain.

Instruction : It can be only done through piecewise function. The only information given is the value of m and n. There is no given function. You have to find one.