{"id":15912,"date":"2019-09-11T21:02:58","date_gmt":"2019-09-11T21:02:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/precalculus\/?post_type=chapter&p=15912"},"modified":"2025-02-05T05:18:06","modified_gmt":"2025-02-05T05:18:06","slug":"problem-set-1","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/precalculus\/chapter\/problem-set-1\/","title":{"raw":"Problem Set 1: Functions and Function Notation","rendered":"Problem Set 1: Functions and Function Notation"},"content":{"raw":"1. What is the difference between a relation and a function?\r\n\r\n2. What is the difference between the input and the output of a function?\r\n\r\n3. Why does the vertical line test tell us whether the graph of a relation represents a function?\r\n\r\n4. How can you determine if a relation is a one-to-one function?\r\n\r\n5. Why does the horizontal line test tell us whether the graph of a function is one-to-one?\r\n\r\nFor the following exercises, determine whether the relation represents a function.\r\n\r\n6. [latex]{(a,b), (c,d), (a,c)}[\/latex]\r\n\r\n7. [latex]{(a,b),(b,c),(c,c)}[\/latex]\r\n\r\nFor the following exercises, determine whether the relation represents [latex]y[\/latex] as a function of [latex]x[\/latex].\r\n\r\n8. [latex]5x+2y=10[\/latex]\r\n\r\n9. [latex]y=x^{2}[\/latex]\r\n\r\n10. [latex]x=y^{2}[\/latex]\r\n\r\n11. [latex]3x^{2}+y=14[\/latex]\r\n\r\n12. [latex]2x+y^{2}=6[\/latex]\r\n\r\n13. [latex]y=\u22122x^{2}+40x[\/latex]\r\n\r\n14. [latex]y=1x[\/latex]\r\n\r\n15. [latex]x=3y+57y\u22121[\/latex]\r\n\r\n16. [latex]x=\\sqrt{1\u2212y^2}[\/latex]\r\n\r\n17. [latex]y=3x+57x\u22121[\/latex]\r\n\r\n18. [latex]x^2+y^2=9[\/latex]\r\n\r\n19. [latex]2xy=1[\/latex]\r\n\r\n20. [latex]x=y^3[\/latex]\r\n\r\n21. [latex]y=x^3[\/latex]\r\n\r\n22. [latex]y=\\sqrt{1\u2212x^2}[\/latex]\r\n\r\n23. [latex]x=\\pm\\sqrt{1\u2212y}[\/latex]\r\n\r\n24. [latex]y=\\pm\\sqrt{1\u2212x}[\/latex]\r\n\r\n25. [latex]y^2=x^2[\/latex]\r\n\r\n26.\u00a0[latex]y^3=x^2[\/latex]\r\n\r\nFor the following exercises, evaluate the function [latex]f[\/latex] at the indicated values [latex]f(\u22123),f(2),f(\u2212a),\u2212f(a),f(a+h)[\/latex].\r\n\r\n27. [latex]f(x)=2x\u22125[\/latex]\r\n\r\n28. [latex]f(x)=\u22125x^2+2x\u22121[\/latex]\r\n\r\n29. [latex]f(x)=\\sqrt{2\u2212x}+5[\/latex]\r\n\r\n30. [latex]f(x)=6x\u221215x+2[\/latex]\r\n\r\n31. [latex]f(x)=|x\u22121|\u2212|x+1|[\/latex]\r\n\r\n32. Given the function\u00a0[latex]g(x)=5\u2212x^{2}[\/latex],evaluate [latex]g(x+h)\u2212g(x)h,h\\ne{0}[\/latex].\r\n\r\n33. Given the function\u00a0[latex]g(x)=x^{2}+2x[\/latex],evaluate [latex]g(x)\u2212g(a)x\u2212a,x\\ne{a}[\/latex].\r\n\r\n34. Given the function\u00a0[latex]k(t)=2t\u22121[\/latex]:\r\n\r\nEvaluate [latex]k(2)[\/latex].\r\n\r\nSolve [latex]k(t)=7[\/latex].\r\n\r\n35. Given the function\u00a0[latex]f(x)=8\u22123x[\/latex]:\r\nEvaluate [latex]f(\u22122)[\/latex].\r\nSolve [latex]f(x)=\u22121[\/latex].\r\n\r\n36. Given the function [latex]p(c)=c^2+c[\/latex]:\r\nEvaluate [latex]p(\u22123)[\/latex].\r\nSolve [latex]p(c)=2[\/latex].\r\n\r\n37. Given the function\u00a0[latex]f(x)=x^2\u22123x[\/latex]:\r\nEvaluate\u00a0[latex]f(5)[\/latex].\r\nSolve\u00a0[latex]f(x)=4[\/latex].\r\n\r\n38. Given the function\u00a0[latex]f(x)=\/sqrt{x+2}[\/latex]:\r\nEvaluate\u00a0[latex]f(7)[\/latex].\r\nSolve\u00a0[latex]f(x)=4[\/latex].\r\n\r\n39. Consider the relationship\u00a0[latex]3r+2t=18[\/latex].\r\nWrite the relationship as a function\u00a0[latex]r=f(t)[\/latex].\r\nEvaluate\u00a0[latex]f(\u22123)[\/latex].\r\nSolve\u00a0[latex]f(t)=2[\/latex].\r\n\r\nFor the following exercises, use the vertical line test to determine which graphs show relations that are functions.\r\n
\r\n
\r\n\r\n40<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n41.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n42<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n43.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n44<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n45.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n46<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n47.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n48<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n49.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n50<\/span>.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n
\r\n\r\n51.<\/span>\r\n
\"Graph<\/span><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n52. Given the following graph,\r\nEvaluate\u00a0[latex]f(\u22121)[\/latex].\r\nSolve for\u00a0[latex]f(x)=3[\/latex].\r\nGraph of relation.\r\n53. Given the following graph,\r\nEvaluate\u00a0[latex]f(0[\/latex]).\r\nSolve for\u00a0[latex]f(x)=\u22123[\/latex]. Graph of relation.\r\n54. Given the following graph,\r\nEvaluate\u00a0[latex]f(4)[\/latex].\r\nSolve for [latex]f(x)=1[\/latex].\r\nGraph of relation.\r\nFor the following exercises, determine if the given graph is a one-to-one function.\r\n\r\n55. Graph of a circle.\r\n56. Graph of a parabola.\r\n57. Graph of a rotated cubic function.\r\n58. Graph of half of 1\/x.\r\n59. Graph of a one-to-one function.\r\n\r\nFor the following exercises, determine whether the relation represents a function.\r\n\r\n60. [latex]{(\u22121,\u22121),(\u22122,\u22122),(\u22123,\u22123)}[\/latex]\r\n\r\n61.\u00a0[latex]{(3,4),(4,5),(5,6)}[\/latex]\r\n\r\n62.\u00a0[latex]{(2,5),(7,11),(15,8),(7,9)}[\/latex]\r\n\r\nFor the following exercises, determine if the relation represented in table form represents [latex]y[\/latex] as a function of [latex]x[\/latex].\r\n\r\n63.\r\nx 5 10 15\r\ny 3 8 14\r\n\r\n64.\r\nx 5 10 15\r\ny 3 8 8\r\n\r\n65.\r\nFor the following exercises, use the function [latex]f[\/latex] represented in the table below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]x[\/latex]<\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/td>\r\n[latex]f<\/span>(<\/span>x<\/span>)[\/latex]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n74<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n28<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n53<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n56<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n36<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n45<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n14<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n47<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n66. Evaluate [latex]f(3)[\/latex].\r\n\r\n67. Solve\u00a0[latex]f(x)=1[\/latex].\r\n\r\nFor the following exercises, evaluate the function\u00a0[latex]f[\/latex] at the values\u00a0[latex]f(\u22122),f(\u22121),f(0),f(1),\\text{ and }f(2)[\/latex].\r\n\r\n68.\u00a0[latex]f(x)=4\u22122x[\/latex]\r\n\r\n69.\u00a0[latex]f(x)=8\u22123x[\/latex]\r\n\r\n70.\u00a0[latex]f(x)=8x^2\u22127x+3[\/latex]\r\n\r\n71. [latex]f(x)=3+\\sqrt{x+3}[\/latex]\r\n\r\n72.\u00a0[latex]f(x)=x\u22122x+3[\/latex]\r\n\r\n73.\u00a0[latex]f(x)=3x[\/latex]\r\n\r\nFor the following exercises, evaluate the expressions, given functions [latex]f,g,\\text{ and }h[\/latex]:\r\n\r\n[latex]f(x)=3x\u22122[\/latex]\r\n[latex]g(x)=5\u2212x^2[\/latex]\r\n[latex]h(x)=\u22122x^2+3x\u22121[\/latex]\r\n\r\n74. [latex]3f(1)\u22124g(\u22122)[\/latex]\r\n\r\n75. [latex]f(73)\u2212h(\u22122)[\/latex]\r\n\r\nFor the following exercises, graph [latex]y=x^2[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.\r\n\r\n76.\u00a0[latex][\u22120.1, 0.1][\/latex]\r\n\r\n77.\u00a0[latex][\u221210, 10][\/latex]\r\n\r\n78.\u00a0[latex][\u2212100,100][\/latex]\r\n\r\nFor the following exercises, graph\u00a0[latex]y=x^{3}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.\r\n\r\n79.\u00a0[latex][\u22120.1, 0.1][\/latex]\r\n\r\n80.\u00a0[latex][\u221210, 10][\/latex]\r\n\r\n81.\u00a0[latex][\u2212100, 100][\/latex]\r\n\r\nFor the following exercises, graph\u00a0[latex]y=\\sqrt{x}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.\r\n\r\n82. [latex][0, 0.01][\/latex]\r\n83.\u00a0[latex][0, 100][\/latex]\r\n84.\u00a0[latex][0, 10,000][\/latex]\r\n\r\nFor the following exercises, graph\u00a0[latex]y=x\\sqrt{3}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.\r\n\r\n85.\u00a0[latex][\u22120.001,0.001][\/latex]\r\n86.\u00a0[latex][\u22121000,1000][\/latex]\r\n87.\u00a0[latex][\u22121,000,000,1,000,000][\/latex]\r\n\r\n88. The amount of garbage, [latex]G[\/latex], produced by a city with population [\/latex]p[\/latex] is given by [\/latex]G=f(p)[\/latex].\u00a0[latex]G[\/latex] is measured in tons per week, and\u00a0[latex]p[\/latex] is measured in thousands of people.\r\nThe town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function\u00a0[latex]f[\/latex].\r\nExplain the meaning of the statement [latex]f(5)=2[\/latex].\r\n\r\n89. The number of cubic yards of dirt,\u00a0[latex]D[\/latex],needed to cover a garden with area a square feet is given by\u00a0[latex]D=g(a)[\/latex].\r\nA garden with area 5000 ft2<\/sup> requires 50 yd<sup>3<\/sup> of dirt. Express this information in terms of the function [latex]g[\/latex].\r\nExplain the meaning of the statement\u00a0[latex]g(100)=1[\/latex].\r\n\r\n90. Let [latex]f(t)[\/latex] be the number of ducks in a lake\u00a0[latex]t[\/latex] years after 1990. Explain the meaning of each statement:\r\n[latex]f(5)=30[\/latex]\r\n[latex]f(10)=40[\/latex]\r\n\r\n91. Let [latex]h(t)[\/latex] be the height above ground, in feet, of a rocket [latex]t[\/latex] seconds after launching. Explain the meaning of each statement:\r\n[latex]h(1)=200[\/latex]\r\n[latex]h(2)=350[\/latex]\r\n\r\n92. Show that the function [latex]f(x)=3(x\u22125)^2+7[\/latex] is not one-to-one.","rendered":"

1. What is the difference between a relation and a function?<\/p>\n

2. What is the difference between the input and the output of a function?<\/p>\n

3. Why does the vertical line test tell us whether the graph of a relation represents a function?<\/p>\n

4. How can you determine if a relation is a one-to-one function?<\/p>\n

5. Why does the horizontal line test tell us whether the graph of a function is one-to-one?<\/p>\n

For the following exercises, determine whether the relation represents a function.<\/p>\n

6. [latex]{(a,b), (c,d), (a,c)}[\/latex]<\/p>\n

7. [latex]{(a,b),(b,c),(c,c)}[\/latex]<\/p>\n

For the following exercises, determine whether the relation represents [latex]y[\/latex] as a function of [latex]x[\/latex].<\/p>\n

8. [latex]5x+2y=10[\/latex]<\/p>\n

9. [latex]y=x^{2}[\/latex]<\/p>\n

10. [latex]x=y^{2}[\/latex]<\/p>\n

11. [latex]3x^{2}+y=14[\/latex]<\/p>\n

12. [latex]2x+y^{2}=6[\/latex]<\/p>\n

13. [latex]y=\u22122x^{2}+40x[\/latex]<\/p>\n

14. [latex]y=1x[\/latex]<\/p>\n

15. [latex]x=3y+57y\u22121[\/latex]<\/p>\n

16. [latex]x=\\sqrt{1\u2212y^2}[\/latex]<\/p>\n

17. [latex]y=3x+57x\u22121[\/latex]<\/p>\n

18. [latex]x^2+y^2=9[\/latex]<\/p>\n

19. [latex]2xy=1[\/latex]<\/p>\n

20. [latex]x=y^3[\/latex]<\/p>\n

21. [latex]y=x^3[\/latex]<\/p>\n

22. [latex]y=\\sqrt{1\u2212x^2}[\/latex]<\/p>\n

23. [latex]x=\\pm\\sqrt{1\u2212y}[\/latex]<\/p>\n

24. [latex]y=\\pm\\sqrt{1\u2212x}[\/latex]<\/p>\n

25. [latex]y^2=x^2[\/latex]<\/p>\n

26.\u00a0[latex]y^3=x^2[\/latex]<\/p>\n

For the following exercises, evaluate the function [latex]f[\/latex] at the indicated values [latex]f(\u22123),f(2),f(\u2212a),\u2212f(a),f(a+h)[\/latex].<\/p>\n

27. [latex]f(x)=2x\u22125[\/latex]<\/p>\n

28. [latex]f(x)=\u22125x^2+2x\u22121[\/latex]<\/p>\n

29. [latex]f(x)=\\sqrt{2\u2212x}+5[\/latex]<\/p>\n

30. [latex]f(x)=6x\u221215x+2[\/latex]<\/p>\n

31. [latex]f(x)=|x\u22121|\u2212|x+1|[\/latex]<\/p>\n

32. Given the function\u00a0[latex]g(x)=5\u2212x^{2}[\/latex],evaluate [latex]g(x+h)\u2212g(x)h,h\\ne{0}[\/latex].<\/p>\n

33. Given the function\u00a0[latex]g(x)=x^{2}+2x[\/latex],evaluate [latex]g(x)\u2212g(a)x\u2212a,x\\ne{a}[\/latex].<\/p>\n

34. Given the function\u00a0[latex]k(t)=2t\u22121[\/latex]:<\/p>\n

Evaluate [latex]k(2)[\/latex].<\/p>\n

Solve [latex]k(t)=7[\/latex].<\/p>\n

35. Given the function\u00a0[latex]f(x)=8\u22123x[\/latex]:
\nEvaluate [latex]f(\u22122)[\/latex].
\nSolve [latex]f(x)=\u22121[\/latex].<\/p>\n

36. Given the function [latex]p(c)=c^2+c[\/latex]:
\nEvaluate [latex]p(\u22123)[\/latex].
\nSolve [latex]p(c)=2[\/latex].<\/p>\n

37. Given the function\u00a0[latex]f(x)=x^2\u22123x[\/latex]:
\nEvaluate\u00a0[latex]f(5)[\/latex].
\nSolve\u00a0[latex]f(x)=4[\/latex].<\/p>\n

38. Given the function\u00a0[latex]f(x)=\/sqrt{x+2}[\/latex]:
\nEvaluate\u00a0[latex]f(7)[\/latex].
\nSolve\u00a0[latex]f(x)=4[\/latex].<\/p>\n

39. Consider the relationship\u00a0[latex]3r+2t=18[\/latex].
\nWrite the relationship as a function\u00a0[latex]r=f(t)[\/latex].
\nEvaluate\u00a0[latex]f(\u22123)[\/latex].
\nSolve\u00a0[latex]f(t)=2[\/latex].<\/p>\n

For the following exercises, use the vertical line test to determine which graphs show relations that are functions.<\/p>\n

\n
\n
\n

40<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

41.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

42<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

43.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

44<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

45.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

46<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

47.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

48<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

49.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

50<\/span>.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n
\n
\n
\n

51.<\/span><\/p>\n

\"Graph<\/span><\/div>\n<\/div>\n<\/section>\n<\/div>\n

52. Given the following graph,
\nEvaluate\u00a0[latex]f(\u22121)[\/latex].
\nSolve for\u00a0[latex]f(x)=3[\/latex].
\nGraph of relation.
\n53. Given the following graph,
\nEvaluate\u00a0[latex]f(0[\/latex]).
\nSolve for\u00a0[latex]f(x)=\u22123[\/latex]. Graph of relation.
\n54. Given the following graph,
\nEvaluate\u00a0[latex]f(4)[\/latex].
\nSolve for [latex]f(x)=1[\/latex].
\nGraph of relation.
\nFor the following exercises, determine if the given graph is a one-to-one function.<\/p>\n

55. Graph of a circle.
\n56. Graph of a parabola.
\n57. Graph of a rotated cubic function.
\n58. Graph of half of 1\/x.
\n59. Graph of a one-to-one function.<\/p>\n

For the following exercises, determine whether the relation represents a function.<\/p>\n

60. [latex]{(\u22121,\u22121),(\u22122,\u22122),(\u22123,\u22123)}[\/latex]<\/p>\n

61.\u00a0[latex]{(3,4),(4,5),(5,6)}[\/latex]<\/p>\n

62.\u00a0[latex]{(2,5),(7,11),(15,8),(7,9)}[\/latex]<\/p>\n

For the following exercises, determine if the relation represented in table form represents [latex]y[\/latex] as a function of [latex]x[\/latex].<\/p>\n

63.
\nx 5 10 15
\ny 3 8 14<\/p>\n

64.
\nx 5 10 15
\ny 3 8 8<\/p>\n

65.
\nFor the following exercises, use the function [latex]f[\/latex] represented in the table below.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
[latex]x[\/latex]<\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/td>\n[latex]f<\/span>(<\/span>x<\/span>)[\/latex]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/td>\n<\/tr>\n
0<\/td>\n74<\/td>\n<\/tr>\n
1<\/td>\n28<\/td>\n<\/tr>\n
2<\/td>\n1<\/td>\n<\/tr>\n
3<\/td>\n53<\/td>\n<\/tr>\n
4<\/td>\n56<\/td>\n<\/tr>\n
5<\/td>\n3<\/td>\n<\/tr>\n
6<\/td>\n36<\/td>\n<\/tr>\n
7<\/td>\n45<\/td>\n<\/tr>\n
8<\/td>\n14<\/td>\n<\/tr>\n
9<\/td>\n47<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

66. Evaluate [latex]f(3)[\/latex].<\/p>\n

67. Solve\u00a0[latex]f(x)=1[\/latex].<\/p>\n

For the following exercises, evaluate the function\u00a0[latex]f[\/latex] at the values\u00a0[latex]f(\u22122),f(\u22121),f(0),f(1),\\text{ and }f(2)[\/latex].<\/p>\n

68.\u00a0[latex]f(x)=4\u22122x[\/latex]<\/p>\n

69.\u00a0[latex]f(x)=8\u22123x[\/latex]<\/p>\n

70.\u00a0[latex]f(x)=8x^2\u22127x+3[\/latex]<\/p>\n

71. [latex]f(x)=3+\\sqrt{x+3}[\/latex]<\/p>\n

72.\u00a0[latex]f(x)=x\u22122x+3[\/latex]<\/p>\n

73.\u00a0[latex]f(x)=3x[\/latex]<\/p>\n

For the following exercises, evaluate the expressions, given functions [latex]f,g,\\text{ and }h[\/latex]:<\/p>\n

[latex]f(x)=3x\u22122[\/latex]
\n[latex]g(x)=5\u2212x^2[\/latex]
\n[latex]h(x)=\u22122x^2+3x\u22121[\/latex]<\/p>\n

74. [latex]3f(1)\u22124g(\u22122)[\/latex]<\/p>\n

75. [latex]f(73)\u2212h(\u22122)[\/latex]<\/p>\n

For the following exercises, graph [latex]y=x^2[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.<\/p>\n

76.\u00a0[latex][\u22120.1, 0.1][\/latex]<\/p>\n

77.\u00a0[latex][\u221210, 10][\/latex]<\/p>\n

78.\u00a0[latex][\u2212100,100][\/latex]<\/p>\n

For the following exercises, graph\u00a0[latex]y=x^{3}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.<\/p>\n

79.\u00a0[latex][\u22120.1, 0.1][\/latex]<\/p>\n

80.\u00a0[latex][\u221210, 10][\/latex]<\/p>\n

81.\u00a0[latex][\u2212100, 100][\/latex]<\/p>\n

For the following exercises, graph\u00a0[latex]y=\\sqrt{x}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.<\/p>\n

82. [latex][0, 0.01][\/latex]
\n83.\u00a0[latex][0, 100][\/latex]
\n84.\u00a0[latex][0, 10,000][\/latex]<\/p>\n

For the following exercises, graph\u00a0[latex]y=x\\sqrt{3}[\/latex] on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.<\/p>\n

85.\u00a0[latex][\u22120.001,0.001][\/latex]
\n86.\u00a0[latex][\u22121000,1000][\/latex]
\n87.\u00a0[latex][\u22121,000,000,1,000,000][\/latex]<\/p>\n

88. The amount of garbage, [latex]G[\/latex], produced by a city with population [\/latex]p[\/latex] is given by [\/latex]G=f(p)[\/latex].\u00a0[latex]G[\/latex] is measured in tons per week, and\u00a0[latex]p[\/latex] is measured in thousands of people.
\nThe town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function\u00a0[latex]f[\/latex].
\nExplain the meaning of the statement [latex]f(5)=2[\/latex].<\/p>\n

89. The number of cubic yards of dirt,\u00a0[latex]D[\/latex],needed to cover a garden with area a square feet is given by\u00a0[latex]D=g(a)[\/latex].
\nA garden with area 5000 ft2<\/sup> requires 50 yd<sup>3<\/sup> of dirt. Express this information in terms of the function [latex]g[\/latex].
\nExplain the meaning of the statement\u00a0[latex]g(100)=1[\/latex].<\/p>\n

90. Let [latex]f(t)[\/latex] be the number of ducks in a lake\u00a0[latex]t[\/latex] years after 1990. Explain the meaning of each statement:
\n[latex]f(5)=30[\/latex]
\n[latex]f(10)=40[\/latex]<\/p>\n

91. Let [latex]h(t)[\/latex] be the height above ground, in feet, of a rocket [latex]t[\/latex] seconds after launching. Explain the meaning of each statement:
\n[latex]h(1)=200[\/latex]
\n[latex]h(2)=350[\/latex]<\/p>\n

92. Show that the function [latex]f(x)=3(x\u22125)^2+7[\/latex] is not one-to-one.<\/p>\n","protected":false},"author":17533,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15912","chapter","type-chapter","status-publish","hentry"],"part":10705,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/15912","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":20,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/15912\/revisions"}],"predecessor-version":[{"id":15939,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/15912\/revisions\/15939"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/10705"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/15912\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=15912"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=15912"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=15912"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=15912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}