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Math 73 Review Test I 1. Solve for the indicated variable. (a) px + mn = −x + b, x (b) g r 2 − = , 4 20 5 r 2.- Solve the following inequalities, graph the solution, and WSUIN. (a) 4(x + 2) + 2x > 5x − 6 (b) 5x + 9 ≥ 4x + 12 and or 8x − 22 ≤ 4x + 6 10(x − 2) ≤ −7 3.- Solve the following absolute value problems and check the answers. ! ! !3 3 !! ! (a) ! + x! = 2 5 10 (b) |5x − 6| = |8x + 10| 4.- Solve the following inequalities and WSUIN. (a) |7x + 1| − 8 ≥ 3 ! ! ! !7 (b) !! x − 5!! + 22 ≤ 2 8 ! ! ! !2 (c)!! x + 1!! ≤ 7[5.0cm] 5 5.- Determine whether the following are functions or not and find the domain and range. (a) {(3, 4), (3, 6), (7, 12), (−2, −2)} (b) {(−3, −3), (4, 6), (−3, 8), (−2, −2)} (c) {(−4, 4), (−2, 4), (3, 9), (−3, 9)} 6.- Graph (and shade) the following inequalities. 5 2 (a) y ≥ − x + 2 5 (b) 5x + 4y ≤ 20 4 5 3 4 2 3 1 2 1 -5 -4 -3 -2 -1 -1 -5 1 2 3 4 5 -2 -3 -4 -3 -2 -1 -1 -2 -3 -4 -4 -5 -5 7.- Find the equation of the line with the given conditions. (a) Passes through (−7, −4), (8, 5) (b) Perpendicular to −3x + 7y = 3 and with x − intercept = 4 (c) Parallel to 7x − 4y = 8 and goes through (2, 3) 1 2 3 4 5 (d) Perpendicular to x = −4 and passing through (2, 5) 8.- Solve the following word problems. (a) Barney is 9 years older than Nemo in 10 years the sum of their ages will be 61. How old are they now? (b) Nacho invests $6, 000 in two accounts. The first account pays 4% annually and the second account pays 5%. If at the end of one year he makes $280 in interest, how much did he invest in each account? 9.- Solve the following word problems. (a) A phone call to China cost $0.75 per minute plus a connection fee of $2.25. How much will it cost to make a 25 minutes call to China? (b) A large cheese pizza costs $10. Each additional topping adds $1.25 to the price. What will be the price of the pizza if you add 4 toppings. 10.- Find the equation of the following lines. y y y x 11.- For g(x) = x x x+2 and f (x) = −x2 + x + 3 find x+1 (a) g[f (0)] (b) f [g(0)] (d) f [f (0)] (c) f [g(−2)] 12.- For f (x) = x2 − x, g(x) = x3 + 9x2 , and h(x) = x−3 5 (a) f ◦ g(x) (b) h ◦ g(x) (c) g ◦ h(x) (d) h ◦ f (x) find (e) h ◦ g(x) (f) g ◦ g(x) 13.- Use the vertical line test to determine if the following are functions or not and find the domain and range. (a) (b) y (c) y x y x x