# Math 18 Final Exam

Math 18 Final Exam (Write your roster number in the box above.) Due: Wednesday, 12-16-2020, 9 p.m. Show necessary work to earn credits. I. Name (A single answer without work won’t earn full credits even if it is correct.) Simplifying the following expressions: (1) −9 − 3(−2 − 5(−7 − 22 )) = (1) (2) −0.24 + 0.9 · (−0.4)2 = (2) (3) (1 32 )2 − 6( 13 − 34 ) = (3) (4) 12 − 3(−5x − 2(3 − 4x)) = (4) 1 II. Sets: (you don’t need to show work.) (5) Let A = {e, n, g, l, i, s, h}, and B = {m, a, t, h}, then, (6) A (b) A B =? S B =? Let C = {x | x < 2} and D = {x | x ≥ −3}, then (a) C (b) C III. T (a) T S D= D= Solving equations: 3x 2 (Show work.) (7) 2| + 1 | −3 = 7 (7) (8) 7 − 2(3x + 2) = 10 + x (8) (9) m+x Solve w = 3x−n for x (9) 2 (10) 2×2 − x − 5 = 0 (10) (11) log(x + 10) = log x + log(x − 2) (11) (12) 32x−5 = (13)  x 2y   2 − 3 = −6 Solve   3x+ y = −10 4 5 5 (Hint: 1 27 (12) (13) multiply both sides of each equation by LCD to eliminate the denominators first.) 3 IV. Solving inequalities: (14) (15) (Show work.) Solve | 5 − 2x |≥ 3 and graph the solution set. (14) q q q q q q q q q q q -5 -4 -3 -2 -1 0 1 2 3 4 5 – Express the solution set of the following compound inequality: (Hint: First, solve each inequality and find its solution set respectively, and then, find their intersection as the answer.) 3x − 7 ≤ 8 AND 5 − 2x ≤ 9 (a) (in set-builder notation:) (b) (graph it on the number line:) V. q q q q q q q q q q q -5 -4 -3 -2 -1 0 1 2 3 4 5 Rectangular system: (16) – (You don’t need to show work.) According to the following graph, answer the questions about the straight line. y6 3 2 1 −3−2−1 0 1 2 −1 −2  r  −3    3   r        (a) Its x-intercept is: (b) Its y-intercept is: x (c) Its slope is: (d) Its equation in Slope-Intercept form is: 4 (17) Lines l1 and l2 are parallel to each other. The equation of Line l1 is x + 2y = −3, and Line l2 is passing through a point (4, 2). y6 (a) Find the equation of l2 in Slope-intercept form: 6 5 4 3 2 1 −6−5−4−3−2−1 0 1 2 3 4 5 6 −1 x −2 (b) Graph the two lines in the rectangular system. −3 −4 −5 −6 VI. Function Basics: (18) (Show work in (b) and (c).) Answer the following questions according to the graph of f (x): f (x) 3 r 2 r 1 r (18a) (b) What is the range? (18b) (c) f (−3) =? (18c) (d) f (3) =? (18d) 6 r −3 −2 −1 (a) What is the domain? 0 1 2 – x 3 (e) for what values of x does f (x) = 1? −1 −2 −3 r (18e) (You can estimate the x value by 0.5, 1.5, · · ·) (19) (f) determine x-intercepts. (18f) (g) determine y-intercept. (18g) f (x) = 3−5x , find its inverse function f −1 (x) 7+x 5 (19) (20) If f (x) = 5 − 3×2 and g(x) = 2x − 7, answer the following questions: (a) f (−0.5) =? (20a) (b) g(x + h) − g(x) =? (20b) (c) (f ◦ g)(x) =? (20c) (d) (g ◦ f )(−3) =? (20d) VII. Quadratic functions: (Show work if required.) (21) Answer the questions about the quadratic functions: and graph it in the rectangular system. y = −x2 + 6x − 3, y6 (a) its opening is: 6 5 (b) its vertex is: 4 3 2 (c) its x-intercept(s) are 1 −6 −5 −4 −3 −2 −1 0 −1 −2 −3 −4 (d) its y-intercept is −5 −6 6 1 2 3 4 5 6 x (22) The graph of the quadratic function y = f (x) = −(x + 5)2 + 8 is a parabola. (a) Is the parabola opening upward or downward? (22a) (b) What point is its vertex? (22b) (c) Does y have a maximum or minimum value and how much is ymax or ymin ? (22c) (d) Find its x-intercepts: (show work.) (22d) (e) Find its y-intercepts: (22e) (f) What is the domain of this function? (22f) (g) What is the range of this function? (22g) VIII. Exponential and Logarithmic functions: (23) Answer the following questions (rounding off to 4 decimal places), using a scientific calculator: (a) 71.5 = (b) 9.1−0.8 = (c) log8 15 = (24) (d) log0.3 2 = If logb x = 5, logb y = −2, and logb z = 12 , then, logb √ x3 y z4 =? Hint: (Expand it first, show work.) 7 (24) (25) Simplifying without using a calculator, show work: log (log 105 + log2 32) = (26) 2 log3 27 + 3 log 100 − 4 log7 7 = (25) (Evaluate each logarithm first, don’t use calculator, show work.) (26) (27) log 25 + log 4 + log 60 − log 6 = (Condense first, don’t use calculator, show work.) (27) (28) Determining whether it is True (T) or False (F): (a) logb (x2 + 9) = 2 logb x + 2 logb 3 (b) logb 27 64 (28a) = 3(logb 3 − logb 4) (28b) (c) log 1000 = 3 (d) logb 3x 2 = (28c) logb 3+logb x 2 (28d) log 9 (e) log b16 = 2 logb 3 − 4 logb 2 b (28e) 8 Math18 Final Exam
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