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PreCalculus Review

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PreCalculus Review-Exam I1. Solve the folowing equations for all solutions, real and complex.(a) 3x2− 17x = 6 3x2+ x −7 = 0(b) x2+ 4x + 8 = 0 x4+ 5x2− 36 = 02. Determing the vertex (point) of the parabola y = x2−3x + 4 and two points on theparabola, one on the left and one on the right of the vertex.3. Given that the vertex of the parabola is (2, −3) and (−1, 4) is another point on theparabola gra ph, determine the function.4. Find the center and the radius o f the circle: x2+ y2+ 6x − 3y = 15. Determine the equation of the line passing thro ug h the points (−2, 1) and (4, 9).6. A rectangle has a perimeter of 60 ft and an area of 144 ft2. What are the dimensions(length and width)?7. A factory offers a retailer 100 calculators at $20 each but will reduce the price by$.05 for each additional calculator over 100 but less than 300. What number ofcalculuators will produce the largest possible sales.8. Let f(x) = x2− |x|, and g(x) =1x, and k(x) =√x + 2.(a) Is f(x) an even function? Is f(x) an odd function?(b) Is g(x) an even function? Is g(x) an odd function?(c) Determine:f(2)g(2) k(g(4)) g(f(−3/10))f ◦ g(2) g ◦ k(4) k(f(0))k(k(2)) f(g(−3/10)) f(k(−1))(d) Determineg(2 + h) −g(2)hand simplify.(e) Determinek(2 + h) −k(2)hand simplify.9. If y =x − 12x + 3determine the inverse f unction.10. Divide:3x4+ 2x3− x2+ 4x + 1x − 211. Divide:2x5− 3x4+ x2− 4x + 5x2+ 112. Show that 3 is a root of the polynomial 2x3−3x2−11x+ 6 and determine the otherroots.13. Solve the inequalities:x3+ 2x2− 15x > 0 |2x −3| ≥ 514. Give the quadratic equation whose roots are12+√32i and12−√32i.15. For the rational function: f(x) =3x2+ x − 1x2− 2x − 15, state the horizontal and

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