VIEWS: 24 PAGES: 5 POSTED ON: 11/23/2011
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