Name                                    

 

Math 154 Practice Exam 2

 

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Key

Problem 1  Write as an exponential function

        log7 x  =  y  

 

Problem 2  Find the value of
log9 27






Problem 3  Find the domain of

            x2 - 5x - 1
                                                    
          x3 - 3x2 + 2x

 

Problem 4

Answer the following True or False.  If True, explain your reasoning, if False, explain your reasoning or show a counter-example.

A.     The exponential function y = bx has y-intercept 1 and the logarithmic function y = logbx has x-intercept 1 for any b >0 with b not equal to 1.

B.     If a graph of a function has two x-intercepts then the function is not 1-1.

 

Problem 5  Let f(x) = 3x + 2, g(x) = x + 3, and c(x) = -1.  Find

 

A)   f ° g (x)  

 

B)       f(x + h) - f(x)
                                                 
                   h

C)   g(f(1))     

 

D)   c ° f (2)     

 

E)      c(x)g(x)
                                           
        f(x) - 7c(x)

 

 

Problem 6  The graphs of y = f(x) and y = g(x) are given below.  Find

A.       f(0)

B.      g(-1)

C.      g ° f (1)  

D.          f(1)
                              
    g(-1)


Problem 7  Find the domain and range of the following functions

A.  f(x)  =  2x-1 + 3

B.  f(x)  =  log8(x+2) - 4

 

Problem 8

Sketch the graph of y = 5x.

 

Problem 9

Solve for w in 

        22w  =  1/256

 

Problem 10

When a certain radioactive element decays, the amount to the element A at any time t is given by

        A  =  25 (2t/1500)

How much of the element will be left after 3000 years?

 

Problem 11

If

f (x)  =   log3(2x - 1)

find

f -1(x)

Problem 12

The graph if the function y = f (x) is shown below.  Determine if this function is 1-1.

Graph of a function that rises up and to the right continuously