Worksheet on Functions

1. Let f(x) and g(x) be given by the following graphs:

    a.  Estimate the domain and range of each function.
       
        Domain of f is [-4,4]. Range of f is [-4,3].

        Domain of g is [-4,4]. Range of g is [-3,2.3] (roughly).


       
    b.  Find 
       
        f(3) = -3.


    c.  Find 
     

    g(-3) = -1.
     
    d.  Find 
       
        (f + g)(1) = f(1) + g(1) = -2 + 1 = -1.
         
    e.  Find 
       
        (f - g)(-1) = f(-1) - g(-1) = -1 - 2 = -3.
         
    f.  Find 
       
        (fg)(4) = f(4) * g(4) = -4 * -3 = 12.
         
    g. Find 
       
        (f/g)(4) = f(4) / g(4) = -4 / -3 = 4/3.
         
    h.  Find 
       
        f o g(2) = f(g(2)) = f(-2) = 0.
         
    i.  Find 
       
        g o f(4) = g(f(4)) = g(-4) = -2.
         
    j.  Find 
      g o g(-3) = g(g(-3)) = g(-1) = 2.  
2.  For each of the following pairs of functions, find  and state the resulting domain for each.
 
a.
         

        The domain for each of the above is all real numbers (since they are all polynomials).
         

    b. 
         

         
         
    c.