honors analysis midterm exam

8/6/2019 Honors Analysis Midterm Exam

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Honors Analysis Midterm Exam

Show all work and box in your answers on your own paper. Organize your work so that it represents a

clear, logical, and easy to follow argument that leads to the correct answer. Any answer, regardless of

the validity, devoid of appropriate work will not receive credit. Good Luck!

1. For the following, state the parent function, and clearly delineate any rigid or non rigidtransformations. Sketch a graph by hand.

a. b. 2. Find ( )( ) f g xo if

2

3( )

2f x

x!

and ( ) 3 g x x! . Also state the domain of ( )( ) f g xo using

interval notation.

3. Find the domain of . State in interval notation.4. Evaluate the piecewise function at the given values and then graph the function.

Find f(-2), f(4), and f(1). Dont forget to graph!

5. Evaluate and simplify the difference quotient for . Explain what thismeans.

6. State the domain of f(x) and the range of g(x). and

7. Find the inverse algebraically for 8. Determine a possible domain restriction that would be needed for this function to be one to

one: .9.

Please change the following function from general form to standard form using the completing

the square process. Then list the vertex and any x intercepts if there are any. If there are no x-

intercepts please state why there are none


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10. Use the leading coefficient test to clearly describe in mathematical terms the end behavior ofthe functions. Also describe how many solutions are possible and how many relative extrema

are possible. Finally, list how many possible negative and positive real roots there are of the

polynomial. Provide reasons for your answers. .11.Find all the zeros of .

12.Write a polynomial equation in simplest form for a function that has:Zeros: -1 (multiplicity 2), Degree: 4 Falls to the left and falls to the right

13.Find the zeros of given a factor is 2x+3.14.Simplify 15.Construct a graph of the following functions. Describe in detail all transformations. List the

asymptote and any intercepts. Finally, list a table of values used and give the domain.

16.Same directions: 17.Evaluate the following without a calculator given that: , , and . Show all steps. Find .18.Solve algebraically: .19.Graph the following rational function using the asymptotes, x-intercepts, y-intercepts, and

holes (points of discontinuity) if there are any. Find the horizontal and vertical asymptotes of

the following. Also list any slant asymptotes if there are any. Finally give the domain and x and

y intercepts if there are any. .20.Find a positive and a negative angle in radians that is coterminal with .

21.Convert the following angle to radians -35522.Given then find .


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23.Evaluate the six trigonometric functions of the given angle (if not possible state that it isundefined):

24.Find the reference angle for the following angles: 322,4.5,

25.The point given is on the terminal side of an angle in standard position. Determine the exactvalues of the six trigonometric functions of the angle: (-5,-6).

26.Given u = and v = -2i - 9j, find the resultant. Put your answer in component form.27.Given u = , find ||u||.28.Given the initial point (tail) of u is (-2,5) and the terminal point (head) is (3,-7) find the direction

or argument of the vector.

29.Find a vector in the direction of and having a magnitude of 4. Put your final answer incomponent form.

30.Determine whether u and v are orthogonal if u = and v = .

Thank you for a great semester!!!!!

honors analysis midterm exam

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