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Intermediate Algebra test one Friday, October 12, 2007 please show your work to get full credit for each problem 1. Is the following a true equation or a false equation? 8 − 6/2 = 2. Write the solutions to the inequality 3 ≤ x < 5 using interval notation. 8−6 2 3. Draw a number line picture of the solutions of the compound inequality x < −2 or x > 2. 4. Evaluate x − y 2 when x = −3 and y = −4. 5. Evaluate x/y when x = 2/3 and y = −5/7. 6. For the function f (x) = 3 + 2x + x2 , (a) evaluate f (0) (b) evaluate f (−4) 7. For which values of x is |x| = −x? 8. Simplify the compound inequality x < 4 and x < 6. 10. Solve the linear equation 9. Solve the linear equation x + 7 = 2x 3 x + .25x = 75 11. Solve the following equation for the variable m: ma = C − mg 12. Solve the linear inequality 45 − 3x ≤ 6 13. Solve the compound inequality 6 < 43 x+2 < 18 14. Solve each absolute value equation: (a) |x| = −2 (b) |2x + 3| = 15 15. Solve each absolute value inequality: (a) |x| ≥ 3 (b) |x − 2007| < 1 2 page two 16. In which of the following graphs is the variable y a function of the variable x? y y (a) y (b) @ @ (c) @ @ x x x 17. In which of the following formulas or tables is the variable y a function of x? (a) y−3x = 6 √ (b) y = ± x (c) x 3 4 5 y 8 9 8 18. A line contains the points (x, y) = (2, 6) and (4, 3). (a) find the line’s slope (b) find an equation for the line 19. A line has slope − 54 and contains the point (x, y) = (−2, 3). Find an equation for the line in point-slope format. 20. Calculate the slope of the line which has equation 3 2 3 x− y = − 7 5 2 21. Given the line y = 4x + 3 (a) state the line’s slope (b) state the slope of a line which is perpendicular to y = 4x + 3 (c) find an equation for the line which is perpendicular to y = 4x + 3 and which passes through the point (−8, 5). 22. Suppose there is a linear relation between the distance travelled in a taxi and the cost of the trip. distance (miles) 12 20 cost $ 30 $ 40 Use the data given above to calculate the cost of a 15 mile trip. 23. A certain house in Yakima has increased in value by 10% from last year’s value. If the house now has a value of $242,000 , calculate its value last year. 24–27. Graph each linear equation & inequality: 24. 4x − 3y = 12 26. y ≥ 5 − 34 x 25. 27. y − 1 = 41 (x + 2) x ≤ 0 and y < −1