Final Exam Review Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 1) f(x) = x2-5 1) A) minimum; 0 B) minimum; -5 C) maximum; - 5 D) maximum; 0 Determine whether the relation represents a function. If it is a function, state the domain and range. 2) 2) Alice Brad Carl snake cat dog A) function domain: {Alice, Brad, Carl} range: {snake, cat, dog} B) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} C) not a function Write the equation in slope-intercept form. 3) 16x + 5y = 3 3) A) y = 16x - 3 B) y = 16 5 x + 3 5 C) y = - 16 5 x + 3 5 D) y = 16 5 x - 3 5 Reduce the rational expression to lowest terms. 4) x2 + 9x + 20 x 2 + 10x + 25 4) A) x + 4 x + 5 B) 9x + 20 10x + 25 C) 9x + 4 10x + 5 D) - x 2 + 9x + 20 x 2 + 10x + 25 Find the domain of the function. 5) f(x) = 12 - x 5) A) {x x 12} B) {x x 2 3} C) {x x 2 3} D) {x x 12} Graph the solution set of the system of inequalities or indicate that the system has no solution. 1
6) y < -x + 5 y > 5x - 3 6) A) B) C) D) 2
Use the slope and y-intercept to graph the linear function. 7) f(x) = 2x - 3 7) A) B) C) D) Graph the circle with radius r and center (h, k). 3
8) r = 3; (h, k) = (3, 0) 8) A) B) C) D) For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 9) f(x) = 3(x + 3)(x - 1)2 9) A) 3, multiplicity 1, touches x-axis; -1, multiplicity 2, crosses x-axis B) -3, multiplicity 1, touches x-axis; 1, multiplicity 2, crosses x-axis C) -3, multiplicity 1, crosses x-axis; 1, multiplicity 2, touches x-axis D) 3, multiplicity 1, crosses x-axis; -1, multiplicity 2, touches x-axis 4
Determine the average rate of change for the function. 10) h(x) = -2x - 4 10) A) -2 B) - 4 C) 2 D) 4 For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 11) 11) A) Absolute maximum: none; Absolute minimum: none B) Absolute maximum: none; Absolute minimum: f(1) = 2 C) Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2 D) Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2 List the intercepts for the graph of the equation. 12) y = x2 + 14x + 48 12) A) (0, 6), (0, 8), (48, 0) B) (0, -6), (0, -8), (48, 0) C) (6, 0), (8, 0), (0, 48) D) (-6, 0), (-8, 0), (0, 48) Simplify the exponential expression. -18x12y7 3 13) 9x 17 y -3 A) -8y 30 x 15 B) 8y 30 x 15 C) -8 x15y30 D) -8y 12 x 15 13) Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. 5
14) 14) A) B) C) D) 6
Find an equation for the line with the given properties. 15) The solid line L contains the point (4, 1) and is perpendicular to the dotted line whose equation is y = 2x. Give the equation of line L in slope-intercept form. 15) A) y - 1 = 2(x - 4) B) y = - 1 2 x + 3 C) y - 1 = - 1 2 (x - 4) D) y = 1 2 x + 3 16) Parallel to the line y = 4x; containing the point (8, 5) 16) A) y - 5 = 4x - 8 B) y = 4x + 27 C) y = 4x - 27 D) y = 4x Solve the problem. 17) Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 111 miles in the same time that Carl travels 96 miles. Rob's trip uses more interstate highways and he can average 5 mph more than Carl. What is Rob's average speed? A) 37 mph B) 34 mph C) 40 mph D) 32 mph 17) 18) A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 5 of the extras? A) 21 B) 1260 C) 2520 D) 42 18) 19) Lisa has 4 skirts, 6 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other? A) 192 possible outfits B) 14 possible outfits C) 24 possible outfits D) 96 possible outfits 19) Find the indicated intercept(s) of the graph of the function. x - 4 20) y-intercept of f(x) = x2 + 5x - 2 20) A) 0, 2 B) (0, 4) C) 0, - 1 2 D) none 7
Give the equation of the horizontal asymptote, if any, of the function. 21) f(x) = 3x 2 + 5 3x2-5 A) y = 3 B) y = 1 C) y = 5 D) no horizontal asymptotes 21) Solve the system by the addition method. 22) 3x + 7y = 12 3x + 2y = 27 A) {(-11, 7)} B) {(-11, 3)} C) {(-3, 11)} D) {(11, -3)} 22) Solve the linear inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 23) 5x - 4 > 4x - 10 23) A) (-6, ) B) (-14, ) C) (-, -6] D) [-6, ) 8
Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 24) 24) A) function domain: all real numbers range: {y y 9} intercepts: (-4, 0), (0, 8), (2, 0) symmetry: none C) function domain: all real numbers range: {y y 9} intercepts: (0, -4), (8, 0), (0, 2) symmetry: none B) function domain: {x x 9} range: all real numbers intercepts: (-4, 0), (0, 8), (2, 0) symmetry: y-axis D) not a function Find the value for the function. 25) Find f(2x) when f(x) = 2x2-5x + 1. 25) A) 8x2-10x + 1 B) 8x2-10x + 2 C) 4x2-10x + 2 D) 4x2-10x + 1 Simplify the expression. Assume that all variables are positive when they appear. 26) -7 2-6 18 26) A) -11 2 B) -13 2 C) 25 2 D) -25 2 27) 48x2y 25 27) A) 4x 3y 5 B) 16x 3y C) x 48y 5 D) 4 3x 2y 5 Solve the equation. 28) 3(x + 1) + 6 = 12 28) A) {-5, 3} B) {-7, 1} C) {-7, 0} D) {-5, 0} 29) x(1 + 3x) = (3x - 1)(x - 3) 29) A) - 3 3 3 B) C) D) - 3 11 121 11 121 9
Solve the radical equation, and check all proposed solutions. 30) 26x - 39 = x + 5 30) A) {-7} B) {8} C) {-8} D) {10} Solve the formula for the indicated variable. 31) S = 2 rh + 2 r2 for h 31) A) h = S - 2 r 2 B) h = 2 (S - r) C) h = S 2 r 2 r - 1 D) h = S - r The function f is one-to-one. Find its inverse. 32) f(x) = 6x + 4 32) A) f-1(x) = x - 4 6 B) f-1(x) = x 6-4 C) f -1(x) = x 6 + 4 D) f -1(x) = x + 4 6 Graph the function. 33) f(x) = -x + 3 if x < 2 2x - 3 if x 2 33) A) B) 10
C) D) List the intercepts of the graph. 34) 34) A) - 2, 0, (-5, 0), 2, 0 B) 0, - 2, (0, -5), 0, 2 C) 0, - 2, (-5, 0), 0, 2 D) - 2, 0, (0, -5), 2, 0 11
The graph of a function f is given. Use the graph to answer the question. 35) For which of the following values of x does f(x) = -4? 35) 5-5 5-5 A) 3 B) 0 C) 2 D) -4 Simplify the expression. 36) (-27)4/3 36) A) -81 B) 81 C) 729 D) not a real number Find the vertical asymptotes of the rational function. x(x - 1) 37) f(x) = x3 + 9x A) x = -3, x = 3 B) x = 0, x = -3, x = 3 C) x = 0 D) x = 0, x = -9 37) Find the domain of the rational function. 38) g(x) = 2x x + 2 A) {x x 0} B) {x x 2} C) {x x -2} D) all real numbers 38) 12
The graph of a function is given. Decide whether it is even, odd, or neither. 39) 39) A) even B) odd C) neither Find the distance between the pair of points. 40) (7, 1) and (-2, -3) 40) A) 5 B) 97 C) 65 D) 36 Solve the equation by factoring. 41) x2-6x - 16 = 0 41) A) {2, -8} B) {2, 8} C) {-2, 8} D) {-2, -8} The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 42) (0, 1) 42) A) constant B) decreasing C) increasing Write the expression in the standard form a + bi. 43) (5 + 8i)(3 + 9i) 43) A) 87-21i B) 72i2 + 69i + 15 C) -57 + 69i D) -57-69i 13
For the function, find the average rate of change of f from 1 to x: f(x) - f(1), x 1 x - 1 44) f(x) = -9x 44) -9 A) -10 B) C) 0 D) -9 x - 1 Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 45) 4x - 6-2 < -5 45) A) -, 9 4 B) 3 4, 9 4 C) -, 3 4 D) Find an equation for the line, in the indicated form, with the given properties. 46) Containing the points (-2, 6) and (-4, 3); slope-intercept form 46) A) y = mx + 9 B) y - 6 = 3 2 (x + 2) C) y = 3 2 x + 9 D) y = - 3 2 x + 9 Simplify the exponential expression. Assume that variables represent nonzero real numbers. xy5-2 47) x 4 y 1 A) B) y 8 C) x10y12 x6 1 x6y11 D) x 6 y8 47) Factor completely. If the polynomial cannot be factored, say it is prime. 48) 15x4-25x2 + 12x2-20 48) A) (5x2-4)(3x2 + 5) B) (5x4 + 4)(3x - 5) C) (15x2-4)(x2 + 5) D) (5x2 + 4)(3x2-5) 14
Find the function. 49) Find the function that is finally graphed after the following transformations are applied to the graph of y = x. The graph is shifted down 6 units, reflected about the x-axis, and finally shifted left 7 units. A) y = -x - 7-6 B) y = - x + 7-6 C) y = - x + 7 + 6 D) y = - x - 7 + 6 49) Find the domain of the composite function f g. 50) f(x) = x; g(x) = 3x + 15 50) A) {x x -5 or x 0} B) {x x is any real number} C) {x x 0} D) {x x -5} 15