Mathematics 098 first test review problems 1. The graph of a relation is drawn to the right y (a) What is the domain of the relation? 2 1 (b) What is the range of the relation? @ @ x -1 (c) Is this the graph of a function? 1 2 3 2. A line L1 is known to have slope equal to 4/7 (a) what is the slope of a second line, L2 which is parallel to the first line, L1 ? (b) what is the slope of a third line, L3 which is perpendicular to the first line, L1 ? 3. True or False: The absolute value equation |x| = −x is valid for all negative values of x. 4. If f (x) = 3x + 5, find the function value f (2). 5. If g(x) = 4x − x2 , find the function value g(−3). 6. Solve for P : A = P rt + P 7. Suppose that the cost y (in dollars) is a linear function of the number x of items manufactured. The following information is known: number x 0 100 cost y 1500 1550 • what is the slope of the line through these two points ? • what does the slope measure in this situation ? (a good answer should include units) • find an equation for the line through these two points 8. Find an equation for the vertical line which passes through the point (3, −5). 9. Find an equation in point-slope format for the line which contains the points (14, −10) and (68, 20). 10. Solve the absolute value inequality: |x − 55| < 2 page two ( 11. Solve the linear system: 5x + 3y = 8 3x + 2y = 9 ) 12. Solve the inequality: 500 − 2x ≥ x + 140 13. A bartender wants to mix a 5% alcohol solution with 25% alcohol solution to obtain two liters of a 10% alcohol solution. How much of the weaker and how much of the stronger alcohol solution must be mixed together? 14. Graph the equation 3x + 2y = 12. 15. Graph the linear inequality x − 2y ≥ 4.