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PRECALCULUS REVIEW SHEET FOR SECTION 1.1 – 1.3 TEST State the property being illustrated by the equation. 1. 2(3 + x) = 2(3) + 2x _______________ 2. 2 + (x + y) = (x + y ) + 2 __________ 3. 8 + 5 is a real number ______________ 4. 8 + (-8) = 0 _____________________ 5. 1(n) = n __________________________ 6. 4(2n) = (4 2)n ___________________ Sketch the graph and write the interval notation for each. 7. –3 < x < 4 8. x > 9 9. 12 x 10. –3 x 5 11. Find the distance between the points (-2, 7) and (8, 3). Leave your answer in radical form. 12. Find the midpoint of the line segment that connects the points (-4, 6) and (-3, -4). 13. Triangle ABC has vertices A(-2, 3), B(3, -4) and C(-4, 1). Prove that the triangle is isosceles, but not equilateral. 14. Find the values of x so that the point (x, 7) is a distance of 13 spaces away from the point (3, -5). 15. Use the graph to answer the following: a. f(-1) = _______ b. f(2) = ________ c. f(x) = 0, x = _____ d. f(x) = 2, x = ________ Give the domain and range of each function. x 21 16. f(x) = x2 – 40 17. f(x) = 18. f(x) = 10x3 – 400x 19. f(x) = -2 - x3 Give the domain of each function. (Challenge yourself on the range) x8 20. f(x) = 3x 2 x 2 6x 5 21. f(x) = x 1 22. Sketch a function with D: [-3, 5] and R: [0, 5]. 23. Sketch a function with a domain of all real numbers and range ( , 2) . 24. Prove that the triangle with vertices (1, 6), (-2, 5), and (2, 3) is a right triangle. 25. Is the triangle with vertices (-1, 4), (5, 6), and (0, 2) equilateral, isosceles, or scalene?