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Math 154 Practice Midterm I

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.

  Printable Key

Problem 1   Solve the inequality.  Write the solution on a number line.

        2x² - 5x > 3

Solution

Problem 2

Solve  x^1/2 + 2x^1/4 - 8  =  0  

Solution

Problem 3 

Graph the following and label the important features:

1. x = -y² + 2    Solution
   

2. y  =  1 +  | x - 2 |     Solution

Problem 4

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

A.      All parabolas y = ax² + bx + c (a non zero) are graphs of functions.

Solution

B.       If the vertex of the parabola y = ax² + bx + c   has positive y-coordinate and the parabola is concave up, then the parabola has two x-intercepts.

Solution

C.     If a graph has two y-intercepts then the graph is not the graph of a function.

Solution

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

A)      f _° g (x)  

Solution

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

Solution

C)        g(f(1))     

Solution

D)      c _° f (2)     

Solution

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

Solution

Problem 6   Consider the function

    f(x)  =  3x - 2

A.  Sketch the graph of f(x) and explain in a complete sentence why the graph indicates that f(x) has an inverse function.

Solution

B.  Find (algebraically) f ^-1 (x).

Solution

Problem 7  (16 Points)  Graph the quadratic function.  Label any intercepts, the vertex, and the axis of symmetry.  State the domain and range.

        y  =  -2x² + 4x + 6

 Solution

Problem 8  The graphs of y = f(x) and y = g(x) are given below.  Find

A.      f(0)

B.    g(-1)

C.  f ^-1 (0)

D.      g _° f (1)  

E.          f(1)
                              
     g(-1)

  Solution

Extra Credit:  Write down one thing that your instructor can do to make the class better and one thing that you feel that the instructor should continue doing.

(Any constructive remarks will be worth full credit.)