Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

Honors Pre-Calculus Non Calculator Review

VIEWS: 24 PAGES: 5

									                           Honors Pre-Calculus Non Calculator Review


SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Graph the function.
       1) f(x) = 3(int (x))




Find the domain of the function.
                      3
       2) f(x) = x -
                     x-2


Find the domain of the indicated combined function.
       3) Find the domain of (fg)(x) when f(x) =   5x + 7 and g(x) =    6x - 7.

For the given functions f and g , find the indicated composition.
       4) f(x) = 9x2 - 9x, g(x) = 11x - 5
          (f g)(4)

                    1                  5
       5) f(x) =       ,      g(x) =
                   x-2                 3x
          (f g)(x)


Graph f as a solid line and f-1 as a dashed line in the same rectangular coordinate space. Use interval notation to give the domain
and range of f and f-1 .
       6) f(x) = (x - 4)2 , x 4




                                                                    1
Find the zeros of the polynomial function.
       7) f(x) = x3 + 3x2 - 4x - 12

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or
touches the x-axis and turns around, at each zero.
       8) f(x) = -3 x + 2 (x + 5)3

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers.
       9) f(x) = 3x3 - 6x - 4; between 1 and 2

Determine the maximum possible number of turning points for the graph of the function.
      10) f(x) = x6 + 2x7


      11) f(x) = (x - 2)(x - 7)(x + 5)(x + 3)

Graph the polynomial function.
               1 1
     12) f(x) = - x4
               2 2




Divide using synthetic division.
      13) (x2 + 10x + 16) ÷ (x + 3)

Use synthetic division and the Remainder Theorem to find the indicated function value.
      14) f(x) = 2x3 - 8x2 - 4x + 1; f(-2)

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the
polynomial equation.
      15) x3 + 3x2 - 6x - 8 = 0; -4

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
      16) f(x) = x3 - 3x2 - x + 3

Find an nth degree polynomial function with real coefficients satisfying the given conditions.
      17) n = 3; 3 and i are zeros; f(2) = 15

Find the domain of the rational function.
                       9x
      18) f(x) =
                 (x + 6)(x + 4)


                                                                   2
Find the vertical asymptotes, if any, of the graph of the rational function.
                    x
      19) f(x) =
                 x(x + 2)


Find the horizontal asymptote, if any, of the graph of the rational function.
                  9x2
      20) g(x) =
                 3x2 + 1


                      9x3
      21) h(x) =
                     3x2 + 1


                       6x
      22) f(x) =
                     2x2 + 1


Find the slant asymptote, if any, of the graph of the rational function.
                 x2 - 9x + 4
      23) f(x) =
                    x+9


Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.
           x-5
      24)       >0
           x+6




            -x - 2
      25)              0
            x+3




Solve the problem.
      26) An arrow is fired straight up from the ground with an initial velocity of 208 feet per second. Its height, s(t), in feet at any
          time t is given by the function s(t) = -16t2 + 208t. Find the interval of time for which the height of the arrow is greater
            than 480 feet.

Evaluate the expression without using a calculator.
                1
      27) log3
                 3


Find the domain of the logarithmic function.
      28) f(x) = ln (3 - x)

Evaluate the expression without using a calculator.
      29) eln 13x5

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic
expressions without using a calculator.
      30) log (1000x)


                                                                     3
                e3
      31) ln
                11


      32) 2ln (x - 9) - 3 ln x

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give
the exact answer.
      33) log       (x + 5) = 3 + log       (x - 2)
                5                       5

Solve the problem.
      34) What is the range of the sine function?

Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators.
                   3         -2 10
       35) sin t = , cos t =       . Find csc t.
                   7           7


                     3           2 10
      36) sin t =      , cos t =      . Find tan t.
                     7            7


Find the exact value of the expression. Do not use a calculator.
      37) If tan      = 8, find the exact value of cot       -   .
                                                         2


Let   be an angle in standard position. Name the quadrant in which the angle     lies.
      38) cot       < 0,   cos   >0

Find the exact value of the indicated trigonometric function of .
                   2
      39) sin = - , tan > 0                 Find sec .
                   5


Determine the amplitude or period as requested.
      40) Period of y = 9 sin 3x -
                                            2


                                             1
      41) Amplitude of y = -5 cos              x
                                             3


Determine the phase shift of the function.
                    1
     42) y = 2 cos ( x + )
                    2   2




                                                                     4
Find an equation for the graph.
      43)




Graph the function.
                        1
      44) y = |3 cos      x|
                        3




      45) y = 2 csc x




An object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in meters .
Find the maximum displacement, the frequency, and the time required for one cycle.
      46) d = -4 sin 3t meters

An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and then released.
Write an equation for the distance of the object from its rest position after t seconds.
      47) amplitude = 6 cm; period = 3 seconds




                                                                 5

								
To top