Math 1910                                                      Graded HW 1

 

 

Due: Tuesday October 6, 2009

 

1. Sketch the graph of the function . Then use horizontal and vertical shifts to sketch the graph of the function . Identify the domain, range and the x- and y-intercepts of  f(x) using interval notation.

 

2. Use the definition of limit to prove that

 

3. Find the following limits

 

            a)

 

            b)

 

4. Find the a such that the following function is continuous on the entire real line

 

           

 

 

5. Find the vertical asymptotes (if any) of the graph of the function . Use interval notation to identify the domain of the function.