1. State the domain for the function. [1.1] h(x) = x2 - 9 2. Let f(x) = x - 2, g(x) = 3x + 4, and h(x) = 3x2 - 2x - 8, and find the fol- lowing. [1.2] a. (fg)(3) b. h(3) c. f(g(3)) 3. For the following straight line, identify the x-intercept, y-intercept, and slope, and sketch the graph. [1.3] 2x+ y = 6 Find the equation for each line. [1.3] 4. Give the equation of the line through (-1, 3) that has slope m = 2. 5. Give the equation of the line through (-3, 2) and (4, -1). Graph the piecewise-defined function. [1.3] 6. f(x) = * - 2 if x = 2 1 ( x - 2)2 if x > 2 7. Use the tables below to determine lim f(x), if it exists. [1.4] x (from the left) f ( x) * (from the right) f (x) 12.5 1.7 13.5 2.2 12.7 1.9 13.3 2.1 12.9 1,99 13.1 2.01 12.99 1.999 13.01 2.001 12.999 1.9999 13.001 2.0001 8. Use the graph to find each limit, if it exists. [1.4] a. lim f(x) b. lim f(x) 6 X-+3 For Problems 9-15, find the indicated limit, if it exists. [1.4] 9. lim 8 x2 - 2x - 8 X-6 10. lim x+1 11. lim x2 - 2x - 3 12. lim 3x3 - 8x X-+3 x - 3 2x 12713. lim 7x2 + 3x - 1 14. lim x4+ 2x3+ x+ 1 *+ 8x2 + x+ 3 x + 3x - 9 15. lim x + 1lx + 10 x+1 For Problems 16 and 17, determine if each illustrated function is discontinuous or continuous at the point x = a. If the function is continuous, so state. If the func- tion is discontinuous, specify the first continuity condition that is not satisfied. [1.5] 16. 17. f (x ) F ( x ) For Problems 18 and 19, discuss the continuity of each function at the specified value of x. If the function is discontinuous, specify the first continuity condition that is not satisfied. [1.5] 18. f(x) = * - 5x - 24 at x = 6 x+3 19. g(x) = 3x - 1 ifx = 1 (x2 - 2x + 5 ifx> 1 at x = 1 20. Find the average rate of change of f(x) with respect to x on the specified in- terval. [1.6] f ( x ) =4 ;on [-1, 1] x+2 21. For f(x) = -3x2 + x - 2, find the difference quotient /(x + h) - f(x) 2. [1.6] h 22. Find the instantaneous rate of change of f(x) at the specified value of x. [1.6] f(x) = 3x2 - 8x + 1; x = 5 23. Find the slope of the tangent line to the graph of the function at the specified point. [1.6] f(x) = *+ 2 x - 6' *=524, \\ g ) W :N' @ Lajos RepasiiStockPhoto 25, @ Warchi/iStockPhoto Health Science: Flu Epidemic Health officials, concerned with a flu epidemic that has hit the north Atlantic coast, have estimated that the number of people ill with flu symptoms can be approximated by the function N(t) = 90t? , 0 = t = 70, where t is measured in days since the beginning of the epidemic. a. How many people will have the flu on day 15? b. What is the average rate of change in the number of people with flu symp- toms from day 40 to day 707 . What is the instantaneous rate of change in the number of people with flu symptoms on day 407 [1.6] N1 10 20 30 40 50 60 70 8O Business: Average Cost A producer and distributor of gift cards produces x boxes of cards per day at an average cost C(x) (in dollars) of 6x + 8,000 Clx) = 2x + 300 a. What is the domain for this function? b. Find C (280). . Find the average rate of change in the average cost, as production increases from 280 boxes/day to 300 boxes/day. d. Find }m; C(x) and explain what your results mean. e. Find i lim C(x) and explain what your results mean with respect to the = |50 graph of the function C if the domain included negative numbers for x. [1.6] 100 200 300 400 500 Boxes