{"id":2282,"date":"2019-05-09T15:36:22","date_gmt":"2019-05-09T15:36:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-dutchess-precalculus\/?post_type=chapter&p=2282"},"modified":"2020-01-14T16:39:39","modified_gmt":"2020-01-14T16:39:39","slug":"1-1-section-exercises","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-dutchess-precalculus\/chapter\/1-1-section-exercises\/","title":{"raw":"1.1 Section Exercises","rendered":"1.1 Section Exercises"},"content":{"raw":"
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1.1 Section Exercises<\/h3>\r\n
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Verbal<\/h4>\r\n
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1. What is the difference between a relation and a function?<\/p>\r\n\r\n<\/div>\r\n

[reveal-answer q=\"fs-id1165137667225\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137667225\"]\r\n

A relation is a set of ordered pairs. A function is a special kind of relation in which no two ordered pairs have the same first coordinate.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165134118515\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165134118515\"]\r\n

When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output. At any particular input value, there can be only one output if the relation is to be a function.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165137679053\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137679053\"]\r\n

When a horizontal line intersects the graph of a function more than once, that indicates that for that output there is more than one input. A function is one-to-one if each output corresponds to only one input.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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Algebraic<\/h4>\r\n

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

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

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

[reveal-answer q=\"fs-id1165135318977\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135318977\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

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

[reveal-answer q=\"fs-id1165137942475\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137942475\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165135675187\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135675187\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165137679348\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137679348\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165135581209\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135581209\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165134042765\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165134042765\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165135434851\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135434851\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165137849364\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137849364\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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23. [latex]x=\u00b1\\sqrt{1-y}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

[reveal-answer q=\"fs-id1165135527680\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135527680\"]\r\n

function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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24. [latex]y=\u00b1\\sqrt{1-x}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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

[reveal-answer q=\"fs-id1165137629243\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137629243\"]\r\n

not a function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

For the following exercises, evaluate the function[latex]\\text{ }f\\text{ }[\/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>\r\n\r\n

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

[reveal-answer q=\"fs-id1165137409631\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137409631\"]\r\n

[latex]\\begin{array}{cccc}f\\left(-3\\right)=-11;& f\\left(2\\right)=-1;& f\\left(-a\\right)=-2a-5;& -f\\left(a\\right)=-2a+5;\\text{ }\\text{ }\\text{ }\\text{ }f\\left(a+h\\right)=2a+2h-5\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165134151868\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165134151868\"]\r\n

[latex]\\begin{array}{cccc}f\\left(-3\\right)=\\sqrt{5}+5;& f\\left(2\\right)=5;& f\\left(-a\\right)=\\sqrt{2+a}+5;& -f\\left(a\\right)=-\\sqrt{2-a}-5;\\text{ }\\text{ }\\text{ }\\text{ }\\text{ }f\\left(a+h\\right)=\\end{array}[\/latex][latex]\\sqrt{2-a-h}+5[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165135357153\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135357153\"]\r\n

[latex]\\begin{array}{cccc}f\\left(-3\\right)=2;& f\\left(2\\right)=1-3=-2;& f\\left(-a\\right)=|-a-1|-|-a+1|;& -f\\left(a\\right)=-|a-1|\\text{ }+|a+1|;\\text{\u2003}\\text{ }f\\left(a+h\\right)=\\text{ }|a+h-1|-|a+h+1|\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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

[reveal-answer q=\"fs-id1165134284461\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165134284461\"]\r\n

[latex]\\frac{g\\left(x\\right)-g\\left(a\\right)}{x-a}=x+a+2,\\text{ }x\\ne a[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

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  1. Evaluate[latex]\\text{ }k\\left(2\\right).[\/latex]<\/li>\r\n \t
  2. Solve[latex]\\text{ }k\\left(t\\right)=7.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
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    35. Given the function[latex]\\text{ }f\\left(x\\right)=8-3x:[\/latex]<\/p>\r\n\r\n

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    1. Evaluate[latex]\\text{ }f\\left(-2\\right).[\/latex]<\/li>\r\n \t
    2. Solve[latex]\\text{ }f\\left(x\\right)=-1.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      [reveal-answer q=\"fs-id1165135518215\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135518215\"]\r\n

      a.[latex]\\text{ }f\\left(-2\\right)=14;\\text{ }[\/latex]b.[latex]\\text{ }x=3[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

        \r\n \t
      1. Evaluate[latex]\\text{ }p\\left(-3\\right).[\/latex]<\/li>\r\n \t
      2. Solve[latex]\\text{ }p\\left(c\\right)=2.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
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        37. Given the function[latex]\\text{ }f\\left(x\\right)={x}^{2}-3x:[\/latex]<\/p>\r\n\r\n

          \r\n \t
        1. Evaluate[latex]\\text{ }f\\left(5\\right).[\/latex]<\/li>\r\n \t
        2. Solve[latex]\\text{ }f\\left(x\\right)=4.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
          [reveal-answer q=\"fs-id1165135453081\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135453081\"]\r\n

          a.[latex]\\text{ }f\\left(5\\right)=10;\\text{ }[\/latex]b.[latex]\\text{ }x=-1\\text{ }[\/latex]or[latex]\\text{ }x=4[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

            \r\n \t
          1. Evaluate[latex]\\text{ }f\\left(7\\right).[\/latex]<\/li>\r\n \t
          2. Solve[latex]\\text{ }f\\left(x\\right)=4.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
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            39. Consider the relationship[latex]\\text{ }3r+2t=18.[\/latex]<\/p>\r\n\r\n

              \r\n \t
            1. Write the relationship as a function[latex]\\text{ }r=f\\left(t\\right).[\/latex]<\/li>\r\n \t
            2. Evaluate[latex]\\text{ }f\\left(-3\\right).[\/latex]<\/li>\r\n \t
            3. Solve[latex]\\text{ }f\\left(t\\right)=2.[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
              [reveal-answer q=\"fs-id1165137767447\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137767447\"]\r\n

              a.[latex]\\text{ }f\\left(t\\right)=6-\\frac{2}{3}t;\\text{ }[\/latex]b.[latex]\\text{ }f\\left(-3\\right)=8;\\text{ }[\/latex]c.[latex]\\text{ }t=6\\text{ }[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

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              Graphical<\/h4>\r\n

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

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              40.<\/span><\/div>\r\n
              \u00a0\"graph<\/span><\/div>\r\n<\/div>\r\n
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              41.\u00a0<\/span><\/div>\r\n
              \"\"<\/div>\r\n
              [reveal-answer q=\"fs-id1165135332505\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135332505\"]\r\n

              not a function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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              42.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n<\/div>\r\n
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              43.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n
              [reveal-answer q=\"fs-id1165137597406\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137597406\"]\r\n

              function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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              44.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n<\/div>\r\n
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              45.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n
              [reveal-answer q=\"fs-id1165137399700\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137399700\"]\r\n

              function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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              46.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n<\/div>\r\n
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              47.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n
              [reveal-answer q=\"fs-id1165135190490\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165135190490\"]\r\n

              function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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              48.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n<\/div>\r\n
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              49.\u00a0<\/span><\/div>\r\n
              \"\"<\/div>\r\n
              [reveal-answer q=\"fs-id1165137911649\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165137911649\"]\r\n

              function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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              50.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n<\/div>\r\n
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              51.\u00a0<\/span><\/div>\r\n
              \"graph<\/div>\r\n
              [reveal-answer q=\"fs-id1165134240963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"fs-id1165134240963\"]\r\n

              function<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n

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