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Math 1010 Section 5 William Malone Review 1 Name: This review will be graded on completion and is due on October 7th. Complete solutions can be found on my website. 1. Use the order of operations to simplify the expression 11 × 2 − 5 ÷ 82 − 10 + 6 ÷ 5 × 7 2. Solve the following equation for x. x3 −4x2 +2x−5 = 12 x(2x2 −8x−3)+5x−11. 3. Perform the addition 3 4 + 85 − 11 . 2 4. Simplify ||3 − 2| − ||16 − 20| − | 12 − 87 |||. 5. Graph on the real number line all solutions to 3x + 1 ≤ x + 3 ≤ 10x + 6. 6. Graph on the real number line all solutions to one or both of the inequalities 3x − 6 ≥ 2x + 5 or x − 21 ≤ 4x + 6. 7. Find all solutions to the equation |3x − 6| = |2x + 1| and check all solutions. 8. Find all solutions to the equation |3x + 1| − |x + 10| = 4 and check all solutions. 9. Graph on the real line all solutions to |2x + 43 | ≥ 10. 10. Graph on the real line all solutions to |3x − 7| ≤ 7. √ 11. Plot the points (3, 4), ( 2, −5), (−e, 8), (−2, −π) on the rectangular coordinate system. 12. Use the point plotting method to graph the equation ||x2 − 4| − 3| on the rectangular coordinate system. 13. Find the distance between the given points as well as the midpoint on the line segment joining them. (3, −4) and (−2, 1). 14. Find the distance between the given points as well as the midpoint on the line segment joining them. (e, −π) and ( 3e , 2π). 15. Find the slope between the points ( −4 , 2 ) and ( 52 , −7 ). 3 10 8 16. Find the equation of the line passing through (−2, 1) with slope 5 and write your answer in General Form. 17. Find the equation of the line passing through (−6, 10) with slope −2 and write your in slope-intercept form. 18. Find the equation of the line passing through the points (2, 1) and ( 25 , 37 ). 19. Find the equation of a line passing through the point (3, −1) with y-intercept 6. 20. Find the equation of a line perpendicular to 3x − 8y + 2 = 0 passing through the point (7,10). 21. Find the equation of a line parallel to 5x − y = 9 passing through the point (-2,1). 22. Graph all solutions to 4x − 5y + 9 ≤ 0 on the rectangular coordinate system. 1 . 23. Find f (−2), f (4), and f (10) where f (x) = 4x2 − 6x + 2x 2x + 2 − 3 ≤ x < 5 24. Find g(−3) and g(10) for the function g(x) = x2 − 4x + 2x ≥ 7 √ 25. Prove or disprove that the equation y 2 − 6y + 10 = 6y( 61 y − 2 + 5x) − x − 3 is a function of x. Remember an equation is a function if we can write it as y = stuf f and to show it is not a function we need to find one x-value such that there are two solutions of the form (x, y) and (x, y 0 ) where y 6= y 0 . 26. Prove or disprove that the equation |y| + y 2 = x + 2 is a function of x. 27. Graph the domain of the function P (x) = line. √ ( x−5)(200x−31x2 − x1 ) √ √ (2x−3) 5x+1 x+3 28. Graph the domain of the function Q(x) = on the real number x−3 −16 < x < −1 on the − x 3x + 7 1 ≥ x ≥ 10 real number line. √ 29. (*)Using shifts and reflections of known graphs graph T (x) = − −x − 3 + 6 on the rectangular coordinate system. Be sure to write down the sequence of transformations that you use. 30. Use substitution to find all solutions to the system of equations 2x − 3y = 6 . 5x − 7y = 11 31. Use elimination to find all solutions to the system of equations 4x − y = 4 . 9x + 2y = 10 32. Graph all solutions to the system of inequalities in the rectangular coordinate x−y ≥4 system 2x − 3y ≤ 1