University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2020
Views:

197

Pages:

21
Author:

ronrulez17qs

Chapter 2 Practice Test inequalities Chapter 2: Functions, Linear equations, and #1 – 10: Solve, be sure to check your answer. 1) 𝑥 + 7 = 9 2) 𝑥 − 3 = −7 3) 2𝑥 = 24 4) 2 3 𝑥 = 10 5) 5𝑥 + 15 = 35 6) 2 5 𝑦−3=1 7) 3𝑥 + 12 = 5𝑥 8) 3𝑦 = 11𝑦 + 40 9) 2(6𝑦 − 4) = 16 10) 5𝑥 + 3(6𝑥 − 7) = 25 11) The sum of 3 consecutive odd integers is 51. Find the integers. If a problem asks for consecutive odd integers the variables will be 𝑭𝒊𝒓𝒔𝒕 𝒏𝒖𝒎𝒃𝒆𝒓: 𝒙 𝑺𝒆𝒄𝒐𝒏𝒅 𝒏𝒖𝒎𝒃𝒆𝒓: 𝒙 + 𝟐 𝑻𝒉𝒊𝒓𝒅 𝒏𝒖𝒎𝒃𝒆𝒓: 𝒙 + 𝟒 𝑭𝒐𝒖𝒓𝒕𝒉 𝒏𝒖𝒎𝒃𝒆𝒓: 𝒙 + 𝟔 𝒂𝒏𝒅 𝒔𝒐 𝒐𝒏, 𝒌𝒆𝒆𝒑 𝒂𝒅𝒅𝒊𝒏𝒈 𝟐 𝒂𝒔 𝒐𝒅𝒅 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒂𝒓𝒆 𝒕𝒘𝒐 𝒂𝒑𝒂𝒓𝒕. 12) The first angle in a triangle is measures 30 less than the second. The third angle is three times as large as the first angle. Find the three angles in the triangle. The sum of angles in all triangles is 180 degrees. Best to let x be the first angle as both angles are compared to the first angle. 13) Complete the table Inequality 𝑥≥5 Graph Interval Notation Plot 5 on number line with solid circle, shade right 𝑥<3 Plot 3 on number line with open circle, shade left −2 < 𝑥 < 4 Plot −𝟐 𝒂𝒏𝒅 𝟒 on number line, both open circles, shade between (4, ∞) Plot 4 on number line with open circle, shade right Plot −𝟐 on number line open circle Plot 3 on number line closed circle, shade between (−2,3] #14 −18: Solve each inequality. Express each answer using an inequality, a graph, and interval notation. 14) 𝑥 + 2 < 6 𝑥<4 (−∞4) 15) −3𝑧 ≤ 15 𝑥 ≥ −5 [−5, ∞) 16) 4𝑥 – 2 > 18 𝑥>5 (5, ∞) 17) −4 ≥ 3𝑥 + 11 𝑥 ≤ −5 (−∞, −5] 18) −7 ≤ 𝑥 + 2 < 5 −9 ≤ 𝑥 < 3 [−9,3) 19) Given the graph of f(x), find the following: a) The domain of f (list individual x’s separated by commas inside {} ) domain {-2, -1, 1, 3, 5, 7} b) The range of the f (list individual y’s separated by commas inside {} ) range {-2, 2, 3, 6, 8} c) 𝑓(3) (find the y-coordinate of point with x = 3) 𝒇(𝟑) = 𝟔 d) 𝑓(−2) (find the y-coordinate of point with x = −2) 𝒇(−𝟐) = 𝟖 e) all values of x such that 𝑓(𝑥) = 3 (find x-coordinate of all points with y-coordinate of 3) 𝒙=𝟏 f) all values of x such that 𝑓(𝑥) = −2 (find x-coordinate of all points with y-coordinate of −2) 𝒙 = −𝟏, 𝟕 20) Find the following: 𝑓 = {(1,2), (2, 7), (−4,2), (5, −4), (−3,5), (6,7)} a) The domain of f (list individual x’s separated by commas inside {} ) domain {-4, -3, 1, 2, 5, 6} b) The range of the f (list individual y’s separated by commas inside {} ) range {-4, 2, 5, 7} c) 𝑓(2) (find the y-coordinate of point with x = 2) 𝒇(𝟐) = 𝟕 d) 𝑓(−4) (find the y-coordinate of point with x = −4) 𝒇(−𝟒) = 𝟐 e) all values of x such that 𝑓(𝑥) = −4 (find x-coordinate of all points with y-coordinate of −4) 𝒙=𝟓 f) all values of x such that 𝑓(𝑥) = 2 (find x-coordinate of all points with y-coordinate of 2) 𝒙 = −𝟒, 𝟏 21) Given the graph of h(x), find the following: a) ℎ(8) (find the y-coordinate of point with x = 8) 𝒉(𝟖) = 𝟐𝟎 b) ℎ(0) (find the y-coordinate of point with x = 0) 𝒉(𝟎) = 𝟒 c) all values of x such that ℎ(𝑥) = 8 (find the y-coordinate of point with x = 8) 𝒙 = −𝟏, 𝟓 d) all values of x such that ℎ(𝑥) = 0 (find the y-coordinate of point with x = 0) 𝒙 = 𝟏, 𝟑 22) 𝑓(𝑥) = 2𝑥 − 5 Find the following: a) 𝑓(3) b) 𝑓(−4) c) 𝑓(𝑥 + 1) #23 – 25: Find the domain and range of function. Write your answer in interval notation. 23) 24) 25) 26) Find the a) interval(s) where the graph is increasing. b) interval(s) where the graph is decreasing. c) the coordinates of local maximum point, if any d) the local maximum value 𝒍𝒐𝒄𝒂𝒍 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒊𝒔 𝒚 = 𝟏𝟒𝟔 𝒘𝒉𝒊𝒄𝒉 𝒐𝒄𝒄𝒖𝒓𝒔 𝒘𝒉𝒆𝒏 𝒙 = −𝟒 e) the coordinates of the local minimum point if any f) the local minimum value 𝒍𝒐𝒄𝒂𝒍 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒊𝒔 𝒚 = −𝟏𝟎𝟗 𝒘𝒉𝒊𝒄𝒉 𝒐𝒄𝒄𝒖𝒓𝒔 𝒘𝒉𝒆𝒏 𝒙 = 𝟒 27) Find the a) interval(s) where the graph is increasing. b) interval(s) where the graph is decreasing. c) the coordinates of local maximum point, if any d) the local maximum value 𝒍𝒐𝒄𝒂𝒍 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒊𝒔 𝒚 = 𝟕𝟔 𝒘𝒉𝒊𝒄𝒉 𝒐𝒄𝒄𝒖𝒓𝒔 𝒘𝒉𝒆𝒏 𝒙 = 𝟑 e) the coordinates of the local minimum point if any f) the local minimum value 𝒍𝒐𝒄𝒂𝒍 𝒎𝒊𝒏𝒊𝒎𝒖𝒎 𝒊𝒔 𝒚 = −𝟏𝟖𝟎 𝒘𝒉𝒊𝒄𝒉 𝒐𝒄𝒄𝒖𝒓𝒔 𝒘𝒉𝒆𝒏 𝒙 = −𝟒