Examples for Graphing curves  of given functions.
Math 1012  (Peh Ng)

The command is Plot[f(x), {x, xmin,xmax}]
Advice: to get a real accurate picture of what the curve looks like, you may have to fool around with xmin and xmax

This is how you can plot the function for Problem 33(c) in 1.7

Here are a few examples:

Plot[(x^2 -2x -8)/(x+2),{x,-3,1}]

Plot[x*(2x-7)*(2x-11),{x,-2,8}]

Absolute value's syntax is Abs[], eg:

Plot[(x-7)/Abs[x-7],{x,5,9}]

Plot[(x^3 + 64)/(x+4),{x,-6,3}]

Plot[(3-Sqrt[x])/(9-x),{x,0,12}]

Plot[(Sqrt[16-x^2])/(x-3),{ x,-4,4}]

Plot[(3+x^2)/(4-x^2), {x,-10,10}]

Plot[(x^2-1)/(2x^2 -5), {x,-5,5}]

Plot[(Abs[x])/x, {x, -5,5}]

Plot[Abs[x+1]+Abs[x-1] -3, {x, -5,5}]

Plot[ (x-Abs[x])/(x^2) +1, {x,-10,10}]

To plot piecewise defined functions, we can first define f(x), then plot f(x) in the following way:

f[x_]:=Piecewise[{{2Cos[x],x≤0},{2Sin[x],0<x≤2π
},{(1/4)*x^2, x > 2π}}];

Plot[f[x],{x,-2π,2π},
		PlotStyle->{{Blue,Thickness[0]}}]

After you named a function and plotted the graph, it is always a good habit to clear the function by doing:

Clear[f,x]

Plot[Piecewise[{{2Cos[x],x≤0},{2Sin[x],0<x≤2π
},{(1/4)*x^2, x > 2π}}],{x,-2π,2π}]