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1. Find the equation of the line that passes through these two points (-3, 2), (5,6) (Answer using slope-intercept form) 1 7 ans: y x 2 2 2. Find the equation of a line that passes through (2, 5) and is parallel to y = -4x + 2(Answer using slope-intercept form) ans: y = -4x + 13 3. Find the equation of a line that passes through (4, -2) and is perpendicular to y = 2x – 3(Answer using slope-intercept form) 1 ans: y x 2 4. Find the domain and range of following functions a) f(x) = -2x + 5 Ans: Domain : all real numbers Range: all real numbers b) f(x) = x2 + 3 Ans: Domain all real numbers Range: all numbers greater than 3 c) f(x) = |2x + 5| ans: Domain: all real numbers Range: al real numbers greater than or equal to 0 5. Find the domain of following functions a) f(x) = x2 – 5x + 7 ans: All real numbers 3 f ( x) 4x 1 ans: all real numbers except -1/4 b) f(x) = |2x + 5| ans: all real numbers 6. Perform indicated algebra operation, given f(x) = 2x – 1 and g(x) = -x + 4 (f+g)(x) (f-g)(x) (f∙g)(x) ans: x + 3 ans: 3x – 5 ans: -2x2 + 9x – 4 2x 1 ans: x4 (f/g)(x) 7.Using same functions from above, calculate, (f+g)(2) ans: 5 (f-g)(3) ans: 4 (f∙g)(-1) ans: -15 (f/g)(5) ans: -9 8. Solve following equations a) 2x = 3(x – 5) + 11 – 5x b) 0.5x + 3 = 0.2(x – 3) 1 4 x 1 3 x 5 2 c) 3 ans: x = -1 ans: x= -1.2 ans: x = -28 8. Solve for variable b ans: b a) x = 5yb b) y ba x x 5y ans: b xy a 9. Simplify following exponential expressions(exponents must be positive numbers) (-3x-2y)(x3y2z)2 ans:-3 x4y5z2 y2 16 y 10 (-4x5y-1)-2 ans: a 5b 3 a 7b b2 2 ans: a 12 x 1 y 4 30 x 6 y 2 4 x 2 y 3 3 4 5x y ans: 2 ans: 2y2 5x 7 25 x10 y 2 16 10. Solve following systems of linear equations (try all different methods – substitution, elimination, matrices, Cramer’s rule) 3x 4 y 5 2 x y 1 1 7 , 5 5 ans: 4 x 5 y 2 8 x 10 y 2 ans: no solution 2 x 3 y 7 4 x 6 y 14 ans: infinitely many solutions 3 11 2 3 x 4 y 12 1 x 7 y 1 18 2 3 ans: (-2, 3) 3x y 2 z 12 2 x 3 y z 5 x 3 y 8 z 22 ans: (3, 1, 2) x y 7 3 y 2 z 9 4 x z 5 ans: (2, 5, -3) 11. Find the determinant of following matrices 2 4 3 5 ans: -2 2 1 1 1 2 1 3 4 3 ans: 2 12. A store sells regular coffee for $8 a pound and gourmet coffee for $14 a pound. To get rid of 40 pounds of the gourmet coffee, a shop keeper makes a blend to put on sale for $10 a pound. How many pounds of regular coffee should he use? Ans: 80lbs 13. Ben invested $28,000 in to two accounts. One account gives 7% return, the other 10%. If the interest was $2,560, how much was in each account? Ans: $8,000 in 7%, $20,000 in 10% 14. A car heads west from a city at 65 miles per hour. At the same time a bus heads west at 50 miles per hour. How long before the two are 37.5 miles apart? Ans: 2.5 hours