Math 165: Assignment 7, Sept. 13, 1999

Exercise 1, p.63

SetOptions[Plot,  AspectRatio -> Automatic];

\(f[x_]\  := \ Floor[x]; 
g[x_]\  := \ Floor[2  x]; \)

Plot[f[x],  {x, -1, 2}]

Plot[g[x],  {x, -1, 2}]

Plot[f[x] + g[x], {x, -1, 2}]

Plot[f[x]  +  g[x/2],  {x, -1, 2}]

Plot[f[x] g[x],  {x, -1, 2}]

Plot[(1/4) f[2  x] g[x/2],  {x, -1, 2}]

Exercise 2, p.63

Plot[x  +  Floor[x],  {x, -2, 2}]

Plot[x  -  Floor[x],  {x, -2, 2}]

Plot[Floor[-x],  {x, -2, 2}]

Plot[2  Floor[x],  {x, -2, 2}]

Plot[Floor[x + (1/2)],  {x, -2, 2}]

Plot[Floor[x] + Floor[x + (1/2)],  {x, -2, 2}]

Exercise 3,  p.64

Plot[Floor[(Sqrt[x])],  {x, 0, 10}]

Plot[Floor[(x^2)],  {x, 0, 3}]

Plot[(Sqrt[Floor])[x],  {x, 0, 10}]

Plot[Floor[x]^2,  {x, 0, 3}]