MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) x 8. C) y = x + 3 2

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1 Precalculus Fall Final Exam Review Name Date Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. Assume that the variables in the denominator are nonzero. 8ab b ) ab a3b7 A) ab B) ab C) 3a b D) a b ) ) x-y - yx-4-3 ) A) y x4 B) x 4 y C) x 8 y D) y x8 Perform the indicated operation. Write the result in standard form. 3) ( + 7i) 3) A) i B) i C) 3-49i D) i Determine the equation of the line described. Put answer in the slope-intercept form, if possible. 4) Through (-, -), perpendicular to x + y = -3 4) A) y = x + B) y = x - 3 C) y = - x + 3 D) y = - x - 3 Describe how to transform the graph of f into the graph of g. ) f(x) = x and g(x) = 0.x ) A) Horizontally shrink the graph of f by a factor of 0. B) Vertically stretch the graph of f by a factor of 0. C) Vertically shrink the graph of f by a factor of 0. D) Horizontally stretch the graph of f by a factor of 0. Find the remainder when f(x) is divided by (x - k) ) f(x) = x3-8x - 3x + 3; k = - ) A) -3 B) 9 C) 0 D) -9 Describe the end behavior of the polynomial function by finding lim f x and lim f x. 7) f x = -x3 + x + 7x - 7 7) A), B), C), D), Find the asymptote(s) of the given function. 8) f(x) = x - 3 vertical asymptotes(s) 8) x + 8x A) x = -8 B) x = 8 C) x = 0, x = -8 D) x = 3

2 9) h(x) = 0x horizontal asymptotes(s) 9) x - 3 A) y = 3 B) None C) y = D) y = 3 Solve the problem. 0) The number of students infected with the flu on a college campus after t days is modeled by the 00 function P(t) =. What is the maximum number of infected students possible? + 39e-0.3t A) B) 400 C) 00 D) 00 ) Suppose the amount of a radioactive element remaining in a sample of 00 milligrams after x years can be described by A(x) = 00e-0.03x. How much is remaining after 380 years? Round the answer to the nearest hundredth of a milligram. A),9.74 milligrams B) 0. milligrams C) 0.3 milligrams D) 0.0 milligrams 0) ) For the given function, find all asymptotes of the type indicated (if there are any) ) f(x) = x - 3x +, slant ) x + 8 A) y = x - B) x = y + 3 C) y = x + D) None Find a slope-intercept form equation for the line. 3) Through the points (, ) and (-, 9) 3) A) y = - x + 7 B) y = - 4x + 7 C) y = - x + 7 D) y = - x - 7 Find a cubic function with the given zeros. 4), -, -4 4) A) f x = x3-4x - x - 8 B) f x = x3 + 4x + x - 8 C) f x = x3 + 4x - x - 8 D) f x = x3 + 4x - x + 8 Use limits to describe the behavior of the rational function near the indicated asymptote. 8 ) f(x) = - x + Describe the behavior of the function near its vertical asymptote. A) lim f(x) =, x - lim f(x) = - B) lim f(x) =, x + x -- lim C) lim f(x) = 0, x -- lim f(x) = 0 D) lim f(x) =, x -+ x -- lim f(x) = x -+ f(x) = - x -+ )

3 Perform the requested operation or operations. ) f(x) = x + 8; g(x) = x - 7 Find f(g(x)). ) A) f(g(x)) = x + B) f(g(x)) = x + C) f(g(x)) = (x + 8)( x - 7) D) f(g(x)) = x - 7 x + 8 Find the exponential function that satisfies the given conditions. 7) Initial mass = g, decreasing at a rate of 3.9% per day 7) A) m(t) = t B) m(t) = 0.9t C) m(t) =.39t D) m(t) =.039t 8) Initial mass = 44 g, halving once every hours 8) t/ A) m(t) = 44 B) m(t) = 44 t t C) m(t) = 44 t/ D) m(t) = 44 Solve the inequality. x + 0 9) - 9) A) x - B) x - C) x - D) x - Find the zeros of the function. 0) f x = 7x3-8x - 3x 0) A) and - B) 0, -, and C) - and D) 0,, and - Solve the inequality graphically. ) 8- x < 9- x ) A) x < B) x < 0 C) x > 0 D) x > Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. ) f(x) = x ) A) Exponential decay function; 0.039% B) Exponential growth function; 0.039% C) Exponential growth function; 03.9% D) Exponential growth function; 3.9% Divide f(x) by d(x), and write a summary statement in the form indicated. 3) f x = x - x + ; d x = x - 3 (Write answer in polynomial form) 3) A) f x = x - 3 x B) f x = x - 3 x C) f x = x D) f x = x

4 Determine algebraically whether the function is even, odd, or neither even nor odd. 4) f(x) = x + x 4) A) Neither B) Odd C) Even Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. ) x + 4; 8x4 + 33x3-4x + x + 4 ) A) No B) Yes State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. ) f(x) = - x ) A) Exponential growth function; lim f(x) = 0; x - B) Exponential decay function; lim f(x) = ; x - C) Exponential growth function; lim f(x) = ; x - lim D) Exponential decay function; lim f(x) = 0; x - lim lim f(x) = lim f(x) = 0 f(x) = 0 f(x) = Using the given zero, find all other zeros of f(x). 7) i is a zero of f(x) = x4-8x3 + 4x - 8x + 3 7) A) -i, 4 + 3, 4-3 B) -i, + 3, - 3 C) -i, , -4-3 D) -i, 4 + 3, 4-3 Solve the equation. 8) -3x - 7x - = 0 8) A) - 7 ± 3 i B) 7 ± 3 C) - 7 ± 3 D) 7 ± 3 i 9) 3( - 3x) = 7 9) A) -3 B) 3 C) 9 D) 9 Find the domain of the given function. x ) f(x) = (x + )(x - 7) A) (-, -4) (-4 -) (-, 7) (7, ) B) All real numbers C) [-4, -) (-, 7) (7, ) D) (0, ) 30) 4

5 Find the zeros of the polynomial function and state the multiplicity of each. 3) f(x) = -x(x - )(x + )3 3) A) -, multiplicity 3; 0, multiplicity ;, multiplicity B) -, multiplicity 3; 0, multiplicity ;, multiplicity ;, multiplicity C) -, multiplicity 3;, multiplicity D) -, multiplicity ;, multiplicity ;, multiplicity Solve the quadratic inequality by graphing an appropriate quadratic function. 3) x - 0x + 0 3) A) [7, ) B) [3, 7] C) (-, 3] [7, ) D) (-, 3] Write the expression in standard form. 33) + 3i + 7i A) i B) i C) i D) i 33)

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