College Algebra Diagnostic Quiz - 2
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1.  Given a one-to-one function, f , and two different numbers, a and b, it is possible that f(a) = y and  f(b) = y. 
 True        False 
2.  Given the function below, find its inverse: 


 
 
3.  Given the function below, find its inverse:


 
 
4.  Given the function below, find its inverse:


 
 
5.  Given the function below:


 

  Which of the following would define the domain such that the function would be one-to-one?

x > 0 
 x > 3 
  x > –3 
 All real nos. 
 
6.  Find the vertex of the parabola associated with the function below.  What is the x-coordinate of the vertex?


 
0 
1 
4 
–4 
 
7.  Find the vertex of the parabola associated with the function below.  What is the y-coordinate of the vertex? 
 
\

 14               –4                   7                   –6 
8.  Given that a parabola has its vertex at (3, 1) and goes through the point (7, –31). 
Derive the corresponding equation in the form:  y = a(x – h)² + k .  What is the value of a?

3                 7                   9               –2 
9.  Which of the following statements is true about any quadratic function?
          Its graph is always a parabola.
          Its graph has exactly two x-intercepts.
          It is a one-to-one function.
          All of these are true.
10.  The graph of a quadratic function always crosses the y-axis.

True             False 
11.  Determine the left and right hand behavior for the following function.


 
Left up, Right up 
Left down, Right down
Left down, Right up 
Left up, Right down 
 
12.  Given the graph shown below, to which of the following functions does it correspond?
 
 
 
13. Find a function that has the following zeros:


 
 
14. Divide the following.  What is your remainder?


 
2 
24x + 5
3x – 15
–2 
 
15.  Divide the following using synthetic division.  What is your remainder?


 
14 
2 
8 
20 
 
16.  Given the following function: 

   Use the remainder theorem to find the value of  f ().

–4
1 
–9 
0 
 
17. Assume that f is a polynomial function, c is a real number and assume that f (c) = 0.  Then which of the following would be true?
 
  c is a zero of f.   c is an x-intercept of f. 
  (x – c) is a factor of f.   All of these are true.
 
18.  Given the function:


  Which of the following is NOT a zero of this function?
 

0 
1 
4 
–6 
 
19.  Given the function:

  Find the zeros of this function.
 

 
20.  Given the function:

  Assuming that x = 2 is a zero of the function, find the remaining zeros.
 

 

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