{"id":10794,"date":"2015-07-10T21:02:04","date_gmt":"2015-07-10T21:02:04","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&p=10794"},"modified":"2021-10-25T03:10:35","modified_gmt":"2021-10-25T03:10:35","slug":"functions-and-function-notation-problem-set","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/functions-and-function-notation-problem-set\/","title":{"raw":"Problem set: Functions and Function Notation","rendered":"Problem set: 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]\\left\\{\\left(a,b\\right),\\text{ }\\left(c,d\\right),\\text{ }\\left(a,c\\right)\\right\\}[\/latex]\r\n\r\n7. [latex]\\left\\{\\left(a,b\\right),\\left(b,c\\right),\\left(c,c\\right)\\right\\}[\/latex]\r\n\r\n \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]3{x}^{2}+y=14[\/latex]\r\n\r\n12. [latex]2x+{y}^{2}=6[\/latex]\r\n\r\n13. [latex]y=-2{x}^{2}+40x[\/latex]\r\n\r\n14. [latex]y=\\frac{1}{x}[\/latex]\r\n\r\n15. [latex]x=\\frac{3y+5}{7y - 1}[\/latex]\r\n\r\n16. [latex]x=\\sqrt{1-{y}^{2}}[\/latex]\r\n\r\n17. [latex]y=\\frac{3x+5}{7x - 1}[\/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-{x}^{2}}[\/latex]\r\n\r\n23. [latex]x=\\pm \\sqrt{1-y}[\/latex]\r\n\r\n24. [latex]y=\\pm \\sqrt{1-x}[\/latex]\r\n\r\n25. [latex]{y}^{2}={x}^{2}[\/latex]\r\n\r\n26. [latex]{y}^{3}={x}^{2}[\/latex]\r\n\r\nFor the following exercises, evaluate the function [latex]f[\/latex] at the indicated values [latex]\\text{ }f\\left(-3\\right),f\\left(2\\right),f\\left(-a\\right),-f\\left(a\\right),f\\left(a+h\\right)[\/latex].\r\n\r\n27. [latex]f\\left(x\\right)=2x - 5[\/latex]\r\n\r\n28. [latex]f\\left(x\\right)=-5{x}^{2}+2x - 1[\/latex]\r\n\r\n29. [latex]f\\left(x\\right)=\\sqrt{2-x}+5[\/latex]\r\n\r\n30. [latex]f\\left(x\\right)=\\frac{6x - 1}{5x+2}[\/latex]\r\n\r\n31. [latex]f\\left(x\\right)=|x - 1|-|x+1|[\/latex]\r\n\r\n32. Given the function [latex]g\\left(x\\right)=5-{x}^{2}[\/latex], evaluate [latex]\\frac{g\\left(x+h\\right)-g\\left(x\\right)}{h},h\\ne 0[\/latex].\r\n\r\n33. Given the function [latex]g\\left(x\\right)={x}^{2}+2x[\/latex], evaluate [latex]\\frac{g\\left(x\\right)-g\\left(a\\right)}{x-a},x\\ne a[\/latex].\r\n\r\n34. Given the function [latex]k\\left(t\\right)=2t - 1:[\/latex]\r\n

a. Evaluate [latex]k\\left(2\\right)[\/latex].\r\nb. Solve [latex]k\\left(t\\right)=7[\/latex].<\/p>\r\n35. Given the function [latex]f\\left(x\\right)=8 - 3x:[\/latex]\r\n

a. Evaluate [latex]f\\left(-2\\right)[\/latex].\r\nb. Solve [latex]f\\left(x\\right)=-1[\/latex].<\/p>\r\n36. Given the function [latex]p\\left(c\\right)={c}^{2}+c:[\/latex]\r\n

a. Evaluate [latex]p\\left(-3\\right)[\/latex].\r\nb. Solve [latex]p\\left(c\\right)=2[\/latex].<\/p>\r\n37. Given the function [latex]f\\left(x\\right)={x}^{2}-3x:[\/latex]\r\n

a. Evaluate [latex]f\\left(5\\right)[\/latex].\r\nb. Solve [latex]f\\left(x\\right)=4[\/latex].<\/p>\r\n38. Given the function [latex]f\\left(x\\right)=\\sqrt{x+2}:[\/latex]\r\n

a. Evaluate [latex]f\\left(7\\right)[\/latex].\r\nb. Solve [latex]f\\left(x\\right)=4[\/latex].<\/p>\r\n39. Consider the relationship [latex]3r+2t=18[\/latex].\r\n

a. Write the relationship as a function [latex]r=f\\left(t\\right)[\/latex].\r\nb. Evaluate [latex]f\\left(-3\\right)[\/latex].\r\nc. Solve [latex]f\\left(t\\right)=2[\/latex].<\/p>\r\nFor the following exercises, use the vertical line test to determine which graphs show relations that are functions.\r\n\r\n40.\r\n\r\n\"Graph\r\n\r\n41.\r\n\r\n\"Graph\r\n\r\n42.\r\n\r\n\"Graph\r\n\r\n43.\r\n\r\n\"Graph\r\n\r\n44.\r\n\r\n\"Graph\r\n\r\n45.\r\n\r\n\"Graph\r\n\r\n46.\r\n\r\n\"Graph\r\n\r\n47.\r\n\r\n\"Graph\r\n\r\n48.\r\n\r\n\"Graph\r\n\r\n49.\r\n\r\n\"Graph\r\n\r\n50.\r\n\r\n\"Graph\r\n\r\n51.\r\n\r\n\"Graph\r\n\r\n52.\u00a0Given the following graph,\r\n

a. Evaluate [latex]f\\left(-1\\right)[\/latex].\r\nb. Solve for [latex]f\\left(x\\right)=3[\/latex].<\/p>\r\n\"Graph\r\n\r\n53.\u00a0Given the following graph,\r\n

a. Evaluate [latex]f\\left(0\\right)[\/latex].\r\nb. Solve for [latex]f\\left(x\\right)=-3[\/latex].<\/p>\r\n\"Graph\r\n\r\n54. Given the following graph,\r\n

a. Evaluate [latex]f\\left(4\\right)[\/latex].\r\nb. Solve for [latex]f\\left(x\\right)=1[\/latex].<\/p>\r\n\"Graph\r\n\r\nFor the following exercises, determine if the given graph is a one-to-one function.\r\n\r\n55.\r\n\r\n\"Graph\r\n\r\n56.\r\n\r\n\"Graph\r\n\r\n57.\r\n\r\n\"Graph\r\n\r\n58.\r\n\r\n\"Graph\r\n\r\n59.\r\n\r\n\"Graph\r\n\r\nFor the following exercises, determine whether the relation represents a function.\r\n\r\n60. [latex]\\left\\{\\left(-1,-1\\right),\\left(-2,-2\\right),\\left(-3,-3\\right)\\right\\}[\/latex]\r\n\r\n61. [latex]\\left\\{\\left(3,4\\right),\\left(4,5\\right),\\left(5,6\\right)\\right\\}[\/latex]\r\n\r\n62. [latex]\\left\\{\\left(2,5\\right),\\left(7,11\\right),\\left(15,8\\right),\\left(7,9\\right)\\right\\}[\/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\n<\/colgroup>\r\n\r\n\r\n\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n5<\/td>\r\n10<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
[latex]y[\/latex]<\/strong><\/td>\r\n3<\/td>\r\n8<\/td>\r\n14<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n64.\r\n
\r\n
\r\n<\/colgroup>\r\n\r\n\r\n\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n5<\/td>\r\n10<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
[latex]y[\/latex]<\/strong><\/td>\r\n3<\/td>\r\n8<\/td>\r\n8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n65.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n<\/colgroup>\r\n\r\n\r\n\r\n
[latex]x[\/latex]<\/strong><\/td>\r\n5<\/td>\r\n10<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
[latex]y[\/latex]<\/strong><\/td>\r\n3<\/td>\r\n8<\/td>\r\n14<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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]<\/strong><\/td>\r\n[latex]f\\left(x\\right)[\/latex] <\/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\\left(3\\right)[\/latex].\r\n\r\n67. Solve [latex]f\\left(x\\right)=1[\/latex].\r\n\r\nFor the following exercises, evaluate the function [latex]f[\/latex] at the values\u00a0[latex]f\\left(-2\\right),f\\left(-1\\right),f\\left(0\\right),f\\left(1\\right)[\/latex], and [latex]f\\left(2\\right)[\/latex].\r\n\r\n68. [latex]f\\left(x\\right)=4 - 2x[\/latex]\r\n\r\n69. [latex]f\\left(x\\right)=8 - 3x[\/latex]\r\n\r\n70. [latex]f\\left(x\\right)=8{x}^{2}-7x+3[\/latex]\r\n\r\n71. [latex]f\\left(x\\right)=3+\\sqrt{x+3}[\/latex]\r\n\r\n72. [latex]f\\left(x\\right)=\\frac{x - 2}{x+3}[\/latex]\r\n\r\n73. [latex]f\\left(x\\right)={3}^{x}[\/latex]\r\n\r\nFor the following exercises, evaluate the expressions, given functions [latex]f,g[\/latex], and [latex]h:[\/latex]\r\n
    \r\n \t
  • [latex]f\\left(x\\right)=3x - 2[\/latex]<\/li>\r\n \t
  • [latex]g\\left(x\\right)=5-{x}^{2}[\/latex]<\/li>\r\n \t
  • [latex]h\\left(x\\right)=-2{x}^{2}+3x - 1[\/latex]<\/li>\r\n<\/ul>\r\n74. [latex]3f\\left(1\\right)-4g\\left(-2\\right)[\/latex]\r\n\r\n75. [latex]f\\left(\\frac{7}{3}\\right)-h\\left(-2\\right)[\/latex]\r\n

    Applications<\/h4>\r\n76. The amount of garbage, [latex]G[\/latex], produced by a city with population [latex]p[\/latex] is given by [latex]G=f\\left(p\\right)[\/latex]. [latex]G[\/latex] is measured in tons per week, and [latex]p[\/latex] is measured in thousands of people.\r\n

    a. The 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 [latex]f[\/latex].\r\nb. Explain the meaning of the statement [latex]f\\left(5\\right)=2[\/latex].<\/p>\r\n77. The number of cubic yards of dirt, [latex]D[\/latex], needed to cover a garden with area [latex]a[\/latex] square feet is given by [latex]D=g\\left(a\\right)[\/latex].\r\n

    a. A garden with area 5000 ft2 requires 50 yd3 of dirt. Express this information in terms of the function [latex]g[\/latex].\r\nb. Explain the meaning of the statement [latex]g\\left(100\\right)=1[\/latex].<\/p>\r\n78. Let [latex]f\\left(t\\right)[\/latex] be the number of ducks in a lake [latex]t[\/latex] years after 1990. Explain the meaning of each statement:\r\n

    a. [latex]f\\left(5\\right)=30[\/latex]\r\nb. [latex]f\\left(10\\right)=40[\/latex]<\/p>\r\n79. Let [latex]h\\left(t\\right)[\/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

    a. [latex]h\\left(1\\right)=200[\/latex]\r\nb. [latex]h\\left(2\\right)=350[\/latex]<\/p>\r\n80. Show that the function [latex]f\\left(x\\right)=3{\\left(x - 5\\right)}^{2}+7[\/latex] is not<\/em> one-to-one.\r\n\r\nSee the next page for the solutions\u00a0to the odd-numbered problems.<\/em><\/span>\r\n\r\n<\/div>\r\n<\/div>","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]\\left\\{\\left(a,b\\right),\\text{ }\\left(c,d\\right),\\text{ }\\left(a,c\\right)\\right\\}[\/latex]<\/p>\n

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

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

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

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

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

    15. [latex]x=\\frac{3y+5}{7y - 1}[\/latex]<\/p>\n

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

    17. [latex]y=\\frac{3x+5}{7x - 1}[\/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-{x}^{2}}[\/latex]<\/p>\n

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

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

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

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

    For the following exercises, evaluate the function [latex]f[\/latex] at the indicated values [latex]\\text{ }f\\left(-3\\right),f\\left(2\\right),f\\left(-a\\right),-f\\left(a\\right),f\\left(a+h\\right)[\/latex].<\/p>\n

    27. [latex]f\\left(x\\right)=2x - 5[\/latex]<\/p>\n

    28. [latex]f\\left(x\\right)=-5{x}^{2}+2x - 1[\/latex]<\/p>\n

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

    30. [latex]f\\left(x\\right)=\\frac{6x - 1}{5x+2}[\/latex]<\/p>\n

    31. [latex]f\\left(x\\right)=|x - 1|-|x+1|[\/latex]<\/p>\n

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

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

    34. Given the function [latex]k\\left(t\\right)=2t - 1:[\/latex]<\/p>\n

    a. Evaluate [latex]k\\left(2\\right)[\/latex].
    \nb. Solve [latex]k\\left(t\\right)=7[\/latex].<\/p>\n

    35. Given the function [latex]f\\left(x\\right)=8 - 3x:[\/latex]<\/p>\n

    a. Evaluate [latex]f\\left(-2\\right)[\/latex].
    \nb. Solve [latex]f\\left(x\\right)=-1[\/latex].<\/p>\n

    36. Given the function [latex]p\\left(c\\right)={c}^{2}+c:[\/latex]<\/p>\n

    a. Evaluate [latex]p\\left(-3\\right)[\/latex].
    \nb. Solve [latex]p\\left(c\\right)=2[\/latex].<\/p>\n

    37. Given the function [latex]f\\left(x\\right)={x}^{2}-3x:[\/latex]<\/p>\n

    a. Evaluate [latex]f\\left(5\\right)[\/latex].
    \nb. Solve [latex]f\\left(x\\right)=4[\/latex].<\/p>\n

    38. Given the function [latex]f\\left(x\\right)=\\sqrt{x+2}:[\/latex]<\/p>\n

    a. Evaluate [latex]f\\left(7\\right)[\/latex].
    \nb. Solve [latex]f\\left(x\\right)=4[\/latex].<\/p>\n

    39. Consider the relationship [latex]3r+2t=18[\/latex].<\/p>\n

    a. Write the relationship as a function [latex]r=f\\left(t\\right)[\/latex].
    \nb. Evaluate [latex]f\\left(-3\\right)[\/latex].
    \nc. Solve [latex]f\\left(t\\right)=2[\/latex].<\/p>\n

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

    40.<\/p>\n

    \"Graph<\/p>\n

    41.<\/p>\n

    \"Graph<\/p>\n

    42.<\/p>\n

    \"Graph<\/p>\n

    43.<\/p>\n

    \"Graph<\/p>\n

    44.<\/p>\n

    \"Graph<\/p>\n

    45.<\/p>\n

    \"Graph<\/p>\n

    46.<\/p>\n

    \"Graph<\/p>\n

    47.<\/p>\n

    \"Graph<\/p>\n

    48.<\/p>\n

    \"Graph<\/p>\n

    49.<\/p>\n

    \"Graph<\/p>\n

    50.<\/p>\n

    \"Graph<\/p>\n

    51.<\/p>\n

    \"Graph<\/p>\n

    52.\u00a0Given the following graph,<\/p>\n

    a. Evaluate [latex]f\\left(-1\\right)[\/latex].
    \nb. Solve for [latex]f\\left(x\\right)=3[\/latex].<\/p>\n

    \"Graph<\/p>\n

    53.\u00a0Given the following graph,<\/p>\n

    a. Evaluate [latex]f\\left(0\\right)[\/latex].
    \nb. Solve for [latex]f\\left(x\\right)=-3[\/latex].<\/p>\n

    \"Graph<\/p>\n

    54. Given the following graph,<\/p>\n

    a. Evaluate [latex]f\\left(4\\right)[\/latex].
    \nb. Solve for [latex]f\\left(x\\right)=1[\/latex].<\/p>\n

    \"Graph<\/p>\n

    For the following exercises, determine if the given graph is a one-to-one function.<\/p>\n

    55.<\/p>\n

    \"Graph<\/p>\n

    56.<\/p>\n

    \"Graph<\/p>\n

    57.<\/p>\n

    \"Graph<\/p>\n

    58.<\/p>\n

    \"Graph<\/p>\n

    59.<\/p>\n

    \"Graph<\/p>\n

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

    60. [latex]\\left\\{\\left(-1,-1\\right),\\left(-2,-2\\right),\\left(-3,-3\\right)\\right\\}[\/latex]<\/p>\n

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

    62. [latex]\\left\\{\\left(2,5\\right),\\left(7,11\\right),\\left(15,8\\right),\\left(7,9\\right)\\right\\}[\/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.<\/p>\n\n\n\n\n\n<\/colgroup>\n\n\n\n
    [latex]x[\/latex]<\/strong><\/td>\n5<\/td>\n10<\/td>\n15<\/td>\n<\/tr>\n
    [latex]y[\/latex]<\/strong><\/td>\n3<\/td>\n8<\/td>\n14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    64.<\/p>\n

    \n
    \n\n\n\n\n\n<\/colgroup>\n\n\n\n
    [latex]x[\/latex]<\/strong><\/td>\n5<\/td>\n10<\/td>\n15<\/td>\n<\/tr>\n
    [latex]y[\/latex]<\/strong><\/td>\n3<\/td>\n8<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    65.<\/p>\n<\/div>\n<\/div>\n

    \n
    \n\n\n\n\n\n<\/colgroup>\n\n\n\n
    [latex]x[\/latex]<\/strong><\/td>\n5<\/td>\n10<\/td>\n10<\/td>\n<\/tr>\n
    [latex]y[\/latex]<\/strong><\/td>\n3<\/td>\n8<\/td>\n14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    For 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]<\/strong><\/td>\n[latex]f\\left(x\\right)[\/latex] <\/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\\left(3\\right)[\/latex].<\/p>\n

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

    For the following exercises, evaluate the function [latex]f[\/latex] at the values\u00a0[latex]f\\left(-2\\right),f\\left(-1\\right),f\\left(0\\right),f\\left(1\\right)[\/latex], and [latex]f\\left(2\\right)[\/latex].<\/p>\n

    68. [latex]f\\left(x\\right)=4 - 2x[\/latex]<\/p>\n

    69. [latex]f\\left(x\\right)=8 - 3x[\/latex]<\/p>\n

    70. [latex]f\\left(x\\right)=8{x}^{2}-7x+3[\/latex]<\/p>\n

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

    72. [latex]f\\left(x\\right)=\\frac{x - 2}{x+3}[\/latex]<\/p>\n

    73. [latex]f\\left(x\\right)={3}^{x}[\/latex]<\/p>\n

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