Mini Exam #1            Review Questions             Name _____________________

 

I. Definitions

            1.  What special property makes a relation a function?

 

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            2. Complete the following definition of an inverse function :

 

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            3. Write the general equation for a sinusoidal function.

 

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II. Sketch the graphs of each of the following:

 

            4.  y = tan(x)

 

            5.   

 

            6.   

 

            7.   

 

 

III. Different kinds of functions have different properties.

 

            8. State the Pythagorean property for sines and cosines (a trig identity).

 

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            9. State the double angle property for cos(x).

 

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            10. State the Quadratic formula.

 

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IV. Proofs are essential in mathematics.

 

            11. Prove:   

 

 

V. The word inverse is important in mathematics.

 

            12. Determine the multiplicative inverse of 7.  _________________________

 

            13. Determine the inverse function of y = 3x + 12 ______________________

 

            14. Determine the inverse secant of  -2.  ______________________________

 

 

VI. Miscellaneous Multiple choice Questions

 

 

 

_____  16.  Which of the following statements is true?

 

                    

 

 

 

 

_____  19.  If a, b, and c represent the sides of a triangle, and h is the altitude to side b,

                    not find the area of the

                   triangle?

 

  

 

 

 

 

 

_____  22.  What is the domain of the function  f   given by   ?

 

                    

 

 

 

 

 

 

 

V. Short Answer Questions

 

24. Transform the following parametric equations to a Cartesian equation by eliminating

          the parameter.

                                    x = 5 cos(t)

                                    y = 5 sin(t)

 

25. Determine the constant  k  and the resulting quadratic factor of    

       if  x  3  is a linear factor.

 

26.  Find the equation of all lines parallel to   5x  3y + 4 = 0.

 

27. Find the real number k for which the solution set of      is the open

      interval   .

 

28.  Determine the solution of   .

 

29.  If