{"id":119,"date":"2026-01-12T15:49:00","date_gmt":"2026-01-12T15:49:00","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=119"},"modified":"2026-01-12T15:49:01","modified_gmt":"2026-01-12T15:49:01","slug":"algebraic-operations-on-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/algebraic-operations-on-functions-get-stronger-answer-key\/","title":{"raw":"Algebraic Operations on Functions: Get Stronger Answer Key","rendered":"Algebraic Operations on Functions: Get Stronger Answer Key"},"content":{"raw":"

Combinations and Compositions of Functions<\/span><\/h2>\r\n
    \r\n \t
  1. [latex](f+g)(x)[\/latex]: [latex]2x+6[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]\r\n[latex](f-g)(x)[\/latex]: [latex]2x^2+2x-6[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]\r\n[latex](fg)(x)[\/latex]: [latex]-x^4-2x^3+6x^2+12x[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]\r\n[latex](\\frac{f}{g})(x)[\/latex]: [latex]\\dfrac{x^2+2x}{6-x^2}[\/latex], domain: [latex](-\\infty,-\\sqrt{6})\\cup(-\\sqrt{6},\\sqrt{6})\\cup(\\sqrt{6},\\infty)[\/latex]<\/li>\r\n \t
  2. [latex](f+g)(x)[\/latex]: [latex]\\dfrac{4x^3+8x^2+1}{2x}[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]\r\n[latex](f-g)(x)[\/latex]: [latex]\\dfrac{4x^3+8x^2-1}{2x}[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]\r\n[latex](fg)(x)[\/latex]: [latex]x+2[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]\r\n[latex](\\frac{f}{g})(x)[\/latex]: [latex]4x^3+8x^2[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]<\/li>\r\n \t
  3. [latex](f+g)(x)[\/latex]: [latex]3x^2+\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]\r\n[latex](f-g)(x)[\/latex]: [latex]3x^2-\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]\r\n[latex](fg)(x)[\/latex]: [latex]3x^2\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]\r\n[latex](\\frac{f}{g})(x)[\/latex]: [latex]\\dfrac{3x^2}{\\sqrt{x-5}}[\/latex], domain: [latex][5,\\infty)[\/latex]\r\n
      \r\n \t
    1. [latex]3[\/latex]<\/li>\r\n \t
    2. [latex]f(g(x))=2(3x-5)^2+1[\/latex]<\/li>\r\n \t
    3. [latex]f(g(x))=6x^2-2[\/latex]<\/li>\r\n \t
    4. [latex](g\\circ g)(x)=3(3x-5)-5=9x-20[\/latex]<\/li>\r\n \t
    5. [latex](f\\circ f)(-2)=163[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    6. [latex]f(g(x))=\\sqrt{x^2+3}+2[\/latex],\r\n[latex]g(f(x))=x+4\\sqrt{x}+7[\/latex]<\/li>\r\n \t
    7. [latex]f(g(x))=\\sqrt[3]{\\dfrac{x+1}{x^3}}=\\dfrac{\\sqrt[3]{x+1}}{x}[\/latex],\r\n[latex]g(f(x))=\\dfrac{\\sqrt[3]{x+1}}{x}[\/latex]<\/li>\r\n \t
    8. [latex](f\\circ g)(x)=\\dfrac{1}{\\frac{2}{x}+4-4}=\\dfrac{x}{2}[\/latex],\r\n[latex](g\\circ f)(x)=2x-4[\/latex]<\/li>\r\n \t
    9. [latex]f(g(h(x)))=(\\dfrac{1}{x+3})^2+1[\/latex]\r\n
        \r\n \t
      1. [latex](g\\circ f)(x)=-\\dfrac{3}{\\sqrt{2-4x}}[\/latex]<\/li>\r\n \t
      2. [latex](-\\infty,\\dfrac{1}{2})[\/latex]<\/li>\r\n<\/ol>\r\n
          \r\n \t
        1. [latex](0,2)\\cup(2,\\infty)[\/latex]<\/li>\r\n \t
        2. [latex](-\\infty,-2)\\cup(2,\\infty)[\/latex]<\/li>\r\n \t
        3. [latex](0,\\infty)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
        4. [latex](1,\\infty)[\/latex]<\/li>\r\n \t
        5. sample: [latex]f(x)=x^3[\/latex] [latex]g(x)=x-5[\/latex]<\/li>\r\n \t
        6. sample: [latex]f(x)=\\dfrac{4}{x}[\/latex] [latex]g(x)=(x+2)^2[\/latex]<\/li>\r\n \t
        7. sample: [latex]f(x)=\\sqrt[3]{x}[\/latex] [latex]g(x)=\\dfrac{1}{2x-3}[\/latex]<\/li>\r\n \t
        8. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=\\dfrac{3x-2}{x+5}[\/latex]<\/li>\r\n \t
        9. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=2x+6[\/latex]<\/li>\r\n \t
        10. sample: [latex]f(x)=\\sqrt[3]{x}[\/latex] [latex]g(x)=(x-1)[\/latex]<\/li>\r\n \t
        11. sample: [latex]f(x)=x^3[\/latex] [latex]g(x)=\\dfrac{1}{x-2}[\/latex]<\/li>\r\n \t
        12. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=\\dfrac{2x-1}{3x+4}[\/latex]<\/li>\r\n \t
        13. [latex]2[\/latex]<\/li>\r\n \t
        14. [latex]5[\/latex]<\/li>\r\n \t
        15. [latex]4[\/latex]<\/li>\r\n \t
        16. [latex]0[\/latex]<\/li>\r\n \t
        17. [latex]2[\/latex]<\/li>\r\n \t
        18. [latex]1[\/latex]<\/li>\r\n \t
        19. [latex]4[\/latex]<\/li>\r\n \t
        20. [latex]4[\/latex]<\/li>\r\n \t
        21. [latex]9[\/latex]<\/li>\r\n \t
        22. [latex]4[\/latex]<\/li>\r\n \t
        23. [latex]2[\/latex]<\/li>\r\n \t
        24. [latex]3[\/latex]<\/li>\r\n \t
        25. [latex]11[\/latex]<\/li>\r\n \t
        26. [latex]0[\/latex]<\/li>\r\n \t
        27. [latex]7[\/latex]<\/li>\r\n \t
        28. [latex]f(g(0))=27[\/latex], [latex]g(f(0))=-94[\/latex]<\/li>\r\n \t
        29. [latex]f(g(0))=\\dfrac{1}{5}[\/latex], [latex]g(f(0))=5[\/latex]<\/li>\r\n \t
        30. [latex]18x^2+60x+51[\/latex]<\/li>\r\n \t
        31. [latex]g\\circ g(x)=9x+20[\/latex]<\/li>\r\n \t
        32. c<\/li>\r\n \t
        33. [latex]A(t)=\\pi(25\\sqrt{t}+2)^2[\/latex] and [latex]A(2)=\\pi(25\\sqrt{4})^2=2500\\pi[\/latex] square inches<\/li>\r\n \t
        34. [latex]A(5)=\\pi(2(5)+1)^2=121\\pi[\/latex] square units\r\n
            \r\n \t
          1. [latex]N(T(t))=23(5t+1.5)^2-56(5t+1.5)+1[\/latex]<\/li>\r\n \t
          2. [latex]3.38[\/latex] hours<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

            Transformations of Functions<\/span><\/h2>\r\n
              \r\n \t
            1. [latex]g(x)=|x-1|-3[\/latex]<\/li>\r\n \t
            2. [latex]g(x)=\\dfrac{1}{(x+4)^2}+2[\/latex]<\/li>\r\n \t
            3. The graph of [latex]f(x+43)[\/latex] is a horizontal shift to the left [latex]43[\/latex] units of the graph of [latex]f[\/latex].<\/li>\r\n \t
            4. The graph of [latex]f(x-4)[\/latex] is a horizontal shift to the right [latex]4[\/latex] units of the graph of [latex]f[\/latex].<\/li>\r\n \t
            5. The graph of [latex]f(x)+8[\/latex] is a vertical shift up [latex]8[\/latex] units of the graph of [latex]f[\/latex].<\/li>\r\n \t
            6. The graph of [latex]f(x)-7[\/latex] is a vertical shift down [latex]7[\/latex] units of the graph of [latex]f[\/latex].<\/li>\r\n \t
            7. The graph of [latex]f(x+4)-1[\/latex] is a horizontal shift to the left [latex]4[\/latex] units and a vertical shift down [latex]1[\/latex] unit of the graph of [latex]f[\/latex].<\/li>\r\n \t
            8. decreasing on latex](-\\infty,-3)[\/latex] and increasing on latex](-3,\\infty)[\/latex]<\/li>\r\n \t
            9. decreasing on latex](0,\\infty)[\/latex]<\/li>\r\n \t
            10. \"Graph<\/li>\r\n \t
            11. \"Graph<\/li>\r\n \t
            12. \"Graph<\/li>\r\n \t
            13. [latex]g(x)=f(x-1)[\/latex], [latex]h(x)=f(x)+1[\/latex]<\/li>\r\n \t
            14. [latex]f(x)=|x-3|-2[\/latex]<\/li>\r\n \t
            15. [latex]f(x)=\\sqrt{x+3}-1[\/latex]<\/li>\r\n \t
            16. [latex]f(x)=(x-2)^2[\/latex]<\/li>\r\n \t
            17. [latex]f(x)=|x+3|-2[\/latex]<\/li>\r\n \t
            18. [latex]f(x)=-\\sqrt{x}[\/latex]<\/li>\r\n \t
            19. [latex]f(x)=-(x+1)^2+2[\/latex]<\/li>\r\n \t
            20. [latex]f(x)=\\sqrt{-x}+1[\/latex]<\/li>\r\n \t
            21. even<\/li>\r\n \t
            22. odd<\/li>\r\n \t
            23. even<\/li>\r\n \t
            24. The graph of [latex]g[\/latex] is a vertical reflection (across the x-axis) of the graph of [latex]f[\/latex].<\/li>\r\n \t
            25. The graph of [latex]g[\/latex] is a vertical stretch by a factor of [latex]4[\/latex] of the graph of [latex]f[\/latex].<\/li>\r\n \t
            26. The graph of [latex]g[\/latex] is a horizontal compression by a factor of [latex]\\dfrac{1}{5}[\/latex] of the graph of [latex]f[\/latex].<\/li>\r\n \t
            27. The graph of [latex]g[\/latex] is a horizontal stretch by a factor of [latex]3[\/latex] of the graph of [latex]f[\/latex].<\/li>\r\n \t
            28. The graph of [latex]g[\/latex] is a horizontal reflection across the [latex]y[\/latex]-axis and a vertical stretch by a factor of [latex]3[\/latex] of the graph of [latex]f[\/latex].<\/li>\r\n \t
            29. [latex]g(x)=|-4x|[\/latex]<\/li>\r\n \t
            30. [latex]g(x)=-\\dfrac{1}{3(x+2)^2}-3[\/latex]<\/li>\r\n \t
            31. [latex]g(x)=\\dfrac{1}{2}(x-5)^2+1[\/latex]<\/li>\r\n \t
            32. The graph of the function [latex]f(x)=x^2[\/latex] is shifted to the left [latex]1[\/latex] unit, stretched vertically by a factor of [latex]4[\/latex], and shifted down [latex]5[\/latex] units.\r\n\"Graph<\/li>\r\n \t
            33. The graph of [latex]f(x)=|x|[\/latex] is stretched vertically by a factor of [latex]2[\/latex], shifted horizontally [latex]4[\/latex] units to the right, reflected across the horizontal axis, and then shifted vertically [latex]3[\/latex] units up.\r\n\"Graph<\/li>\r\n \t
            34. The graph of the function [latex]f(x)=x^3[\/latex] is compressed vertically by a factor of [latex]\\dfrac{1}{2}[\/latex].\r\n\"Graph<\/li>\r\n \t
            35. The graph of the function is stretched horizontally by a factor of [latex]3[\/latex] and then shifted vertically downward by [latex]3[\/latex] units.\r\n\"Graph<\/li>\r\n \t
            36. The graph of [latex]f(x)=\\sqrt{x}[\/latex] is shifted right [latex]4[\/latex] units and then reflected across the vertical line [latex]x=4[\/latex].\r\n\"Graph<\/li>\r\n \t
            37. \"Graph<\/li>\r\n \t
            38. \"Graph<\/li>\r\n<\/ol>\r\n

              Inverse Functions<\/span><\/h2>\r\n
                \r\n \t
              1. [latex]f^{-1}(x)=x-3[\/latex]<\/li>\r\n \t
              2. [latex]f^{-1}(x)=2-x[\/latex]<\/li>\r\n \t
              3. [latex]f^{-1}(x)=\\dfrac{-2x}{x-1}[\/latex]<\/li>\r\n \t
              4. domain of [latex]f(x):[\u22127,\\infty)[\/latex]; [latex]f^{-1}(x)=\\sqrt{x}-7[\/latex]<\/li>\r\n \t
              5. domain of [latex]f(x):[0,\\infty)[\/latex]; [latex]f^{-1}(x)=\\sqrt{x+5}[\/latex]<\/li>\r\n \t
              6. [latex]f(g(x))=x[\/latex], [latex]g(f(x))=x[\/latex]<\/li>\r\n \t
              7. one-to-one<\/li>\r\n \t
              8. one-to-one<\/li>\r\n \t
              9. not one-to-one<\/li>\r\n \t
              10. [latex]3[\/latex]<\/li>\r\n \t
              11. [latex]2[\/latex]<\/li>\r\n \t
              12. \"Graph<\/li>\r\n \t
              13. [latex][2,10][\/latex]<\/li>\r\n \t
              14. [latex]6[\/latex]<\/li>\r\n \t
              15. [latex]-4[\/latex]<\/li>\r\n \t
              16. [latex]0[\/latex]<\/li>\r\n \t
              17. [latex]1[\/latex]<\/li>\r\n \t
              18. \r\n\r\n\r\n\r\n\r\n
                [latex]x[\/latex]<\/th>\r\n[latex]1[\/latex]<\/td>\r\n[latex]4[\/latex]<\/td>\r\n[latex]7[\/latex]<\/td>\r\n[latex]12[\/latex]<\/td>\r\n[latex]16[\/latex]<\/td>\r\n<\/tr>\r\n
                [latex]f^{-1}(x)[\/latex]<\/th>\r\n[latex]3[\/latex]<\/td>\r\n[latex]6[\/latex]<\/td>\r\n[latex]9[\/latex]<\/td>\r\n[latex]13[\/latex]<\/td>\r\n[latex]14[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
              19. [latex]f^{-1}(x)=\\dfrac{5}{9}(x-32)[\/latex]. Given the Fahrenheit temperature, [latex]x[\/latex], this formula allows you to calculate the Celsius temperature.<\/li>\r\n \t
              20. [latex]t(d)=\\dfrac{d}{50}[\/latex], [latex]t(180)=\\dfrac{180}{50}[\/latex]. The time for the car to travel [latex]180[\/latex] miles is [latex]3.6[\/latex] hours.<\/li>\r\n<\/ol>","rendered":"

                Combinations and Compositions of Functions<\/span><\/h2>\n
                  \n
                1. [latex](f+g)(x)[\/latex]: [latex]2x+6[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]
                  \n[latex](f-g)(x)[\/latex]: [latex]2x^2+2x-6[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]
                  \n[latex](fg)(x)[\/latex]: [latex]-x^4-2x^3+6x^2+12x[\/latex], domain: [latex](-\\infty,\\infty)[\/latex]
                  \n[latex](\\frac{f}{g})(x)[\/latex]: [latex]\\dfrac{x^2+2x}{6-x^2}[\/latex], domain: [latex](-\\infty,-\\sqrt{6})\\cup(-\\sqrt{6},\\sqrt{6})\\cup(\\sqrt{6},\\infty)[\/latex]<\/li>\n
                2. [latex](f+g)(x)[\/latex]: [latex]\\dfrac{4x^3+8x^2+1}{2x}[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]
                  \n[latex](f-g)(x)[\/latex]: [latex]\\dfrac{4x^3+8x^2-1}{2x}[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]
                  \n[latex](fg)(x)[\/latex]: [latex]x+2[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]
                  \n[latex](\\frac{f}{g})(x)[\/latex]: [latex]4x^3+8x^2[\/latex], domain: [latex](-\\infty,0)\\cup(0,\\infty)[\/latex]<\/li>\n
                3. [latex](f+g)(x)[\/latex]: [latex]3x^2+\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]
                  \n[latex](f-g)(x)[\/latex]: [latex]3x^2-\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]
                  \n[latex](fg)(x)[\/latex]: [latex]3x^2\\sqrt{x-5}[\/latex], domain: [latex][5,\\infty)[\/latex]
                  \n[latex](\\frac{f}{g})(x)[\/latex]: [latex]\\dfrac{3x^2}{\\sqrt{x-5}}[\/latex], domain: [latex][5,\\infty)[\/latex]<\/p>\n
                    \n
                  1. [latex]3[\/latex]<\/li>\n
                  2. [latex]f(g(x))=2(3x-5)^2+1[\/latex]<\/li>\n
                  3. [latex]f(g(x))=6x^2-2[\/latex]<\/li>\n
                  4. [latex](g\\circ g)(x)=3(3x-5)-5=9x-20[\/latex]<\/li>\n
                  5. [latex](f\\circ f)(-2)=163[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                  6. [latex]f(g(x))=\\sqrt{x^2+3}+2[\/latex],
                    \n[latex]g(f(x))=x+4\\sqrt{x}+7[\/latex]<\/li>\n
                  7. [latex]f(g(x))=\\sqrt[3]{\\dfrac{x+1}{x^3}}=\\dfrac{\\sqrt[3]{x+1}}{x}[\/latex],
                    \n[latex]g(f(x))=\\dfrac{\\sqrt[3]{x+1}}{x}[\/latex]<\/li>\n
                  8. [latex](f\\circ g)(x)=\\dfrac{1}{\\frac{2}{x}+4-4}=\\dfrac{x}{2}[\/latex],
                    \n[latex](g\\circ f)(x)=2x-4[\/latex]<\/li>\n
                  9. [latex]f(g(h(x)))=(\\dfrac{1}{x+3})^2+1[\/latex]\n
                      \n
                    1. [latex](g\\circ f)(x)=-\\dfrac{3}{\\sqrt{2-4x}}[\/latex]<\/li>\n
                    2. [latex](-\\infty,\\dfrac{1}{2})[\/latex]<\/li>\n<\/ol>\n
                        \n
                      1. [latex](0,2)\\cup(2,\\infty)[\/latex]<\/li>\n
                      2. [latex](-\\infty,-2)\\cup(2,\\infty)[\/latex]<\/li>\n
                      3. [latex](0,\\infty)[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                      4. [latex](1,\\infty)[\/latex]<\/li>\n
                      5. sample: [latex]f(x)=x^3[\/latex] [latex]g(x)=x-5[\/latex]<\/li>\n
                      6. sample: [latex]f(x)=\\dfrac{4}{x}[\/latex] [latex]g(x)=(x+2)^2[\/latex]<\/li>\n
                      7. sample: [latex]f(x)=\\sqrt[3]{x}[\/latex] [latex]g(x)=\\dfrac{1}{2x-3}[\/latex]<\/li>\n
                      8. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=\\dfrac{3x-2}{x+5}[\/latex]<\/li>\n
                      9. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=2x+6[\/latex]<\/li>\n
                      10. sample: [latex]f(x)=\\sqrt[3]{x}[\/latex] [latex]g(x)=(x-1)[\/latex]<\/li>\n
                      11. sample: [latex]f(x)=x^3[\/latex] [latex]g(x)=\\dfrac{1}{x-2}[\/latex]<\/li>\n
                      12. sample: [latex]f(x)=\\sqrt{x}[\/latex] [latex]g(x)=\\dfrac{2x-1}{3x+4}[\/latex]<\/li>\n
                      13. [latex]2[\/latex]<\/li>\n
                      14. [latex]5[\/latex]<\/li>\n
                      15. [latex]4[\/latex]<\/li>\n
                      16. [latex]0[\/latex]<\/li>\n
                      17. [latex]2[\/latex]<\/li>\n
                      18. [latex]1[\/latex]<\/li>\n
                      19. [latex]4[\/latex]<\/li>\n
                      20. [latex]4[\/latex]<\/li>\n
                      21. [latex]9[\/latex]<\/li>\n
                      22. [latex]4[\/latex]<\/li>\n
                      23. [latex]2[\/latex]<\/li>\n
                      24. [latex]3[\/latex]<\/li>\n
                      25. [latex]11[\/latex]<\/li>\n
                      26. [latex]0[\/latex]<\/li>\n
                      27. [latex]7[\/latex]<\/li>\n
                      28. [latex]f(g(0))=27[\/latex], [latex]g(f(0))=-94[\/latex]<\/li>\n
                      29. [latex]f(g(0))=\\dfrac{1}{5}[\/latex], [latex]g(f(0))=5[\/latex]<\/li>\n
                      30. [latex]18x^2+60x+51[\/latex]<\/li>\n
                      31. [latex]g\\circ g(x)=9x+20[\/latex]<\/li>\n
                      32. c<\/li>\n
                      33. [latex]A(t)=\\pi(25\\sqrt{t}+2)^2[\/latex] and [latex]A(2)=\\pi(25\\sqrt{4})^2=2500\\pi[\/latex] square inches<\/li>\n
                      34. [latex]A(5)=\\pi(2(5)+1)^2=121\\pi[\/latex] square units\n
                          \n
                        1. [latex]N(T(t))=23(5t+1.5)^2-56(5t+1.5)+1[\/latex]<\/li>\n
                        2. [latex]3.38[\/latex] hours<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                          Transformations of Functions<\/span><\/h2>\n
                            \n
                          1. [latex]g(x)=|x-1|-3[\/latex]<\/li>\n
                          2. [latex]g(x)=\\dfrac{1}{(x+4)^2}+2[\/latex]<\/li>\n
                          3. The graph of [latex]f(x+43)[\/latex] is a horizontal shift to the left [latex]43[\/latex] units of the graph of [latex]f[\/latex].<\/li>\n
                          4. The graph of [latex]f(x-4)[\/latex] is a horizontal shift to the right [latex]4[\/latex] units of the graph of [latex]f[\/latex].<\/li>\n
                          5. The graph of [latex]f(x)+8[\/latex] is a vertical shift up [latex]8[\/latex] units of the graph of [latex]f[\/latex].<\/li>\n
                          6. The graph of [latex]f(x)-7[\/latex] is a vertical shift down [latex]7[\/latex] units of the graph of [latex]f[\/latex].<\/li>\n
                          7. The graph of [latex]f(x+4)-1[\/latex] is a horizontal shift to the left [latex]4[\/latex] units and a vertical shift down [latex]1[\/latex] unit of the graph of [latex]f[\/latex].<\/li>\n
                          8. decreasing on latex](-\\infty,-3)[\/latex] and increasing on latex](-3,\\infty)[\/latex]<\/li>\n
                          9. decreasing on latex](0,\\infty)[\/latex]<\/li>\n
                          10. \"Graph<\/li>\n
                          11. \"Graph<\/li>\n
                          12. \"Graph<\/li>\n
                          13. [latex]g(x)=f(x-1)[\/latex], [latex]h(x)=f(x)+1[\/latex]<\/li>\n
                          14. [latex]f(x)=|x-3|-2[\/latex]<\/li>\n
                          15. [latex]f(x)=\\sqrt{x+3}-1[\/latex]<\/li>\n
                          16. [latex]f(x)=(x-2)^2[\/latex]<\/li>\n
                          17. [latex]f(x)=|x+3|-2[\/latex]<\/li>\n
                          18. [latex]f(x)=-\\sqrt{x}[\/latex]<\/li>\n
                          19. [latex]f(x)=-(x+1)^2+2[\/latex]<\/li>\n
                          20. [latex]f(x)=\\sqrt{-x}+1[\/latex]<\/li>\n
                          21. even<\/li>\n
                          22. odd<\/li>\n
                          23. even<\/li>\n
                          24. The graph of [latex]g[\/latex] is a vertical reflection (across the x-axis) of the graph of [latex]f[\/latex].<\/li>\n
                          25. The graph of [latex]g[\/latex] is a vertical stretch by a factor of [latex]4[\/latex] of the graph of [latex]f[\/latex].<\/li>\n
                          26. The graph of [latex]g[\/latex] is a horizontal compression by a factor of [latex]\\dfrac{1}{5}[\/latex] of the graph of [latex]f[\/latex].<\/li>\n
                          27. The graph of [latex]g[\/latex] is a horizontal stretch by a factor of [latex]3[\/latex] of the graph of [latex]f[\/latex].<\/li>\n
                          28. The graph of [latex]g[\/latex] is a horizontal reflection across the [latex]y[\/latex]-axis and a vertical stretch by a factor of [latex]3[\/latex] of the graph of [latex]f[\/latex].<\/li>\n
                          29. [latex]g(x)=|-4x|[\/latex]<\/li>\n
                          30. [latex]g(x)=-\\dfrac{1}{3(x+2)^2}-3[\/latex]<\/li>\n
                          31. [latex]g(x)=\\dfrac{1}{2}(x-5)^2+1[\/latex]<\/li>\n
                          32. The graph of the function [latex]f(x)=x^2[\/latex] is shifted to the left [latex]1[\/latex] unit, stretched vertically by a factor of [latex]4[\/latex], and shifted down [latex]5[\/latex] units.
                            \n\"Graph<\/li>\n
                          33. The graph of [latex]f(x)=|x|[\/latex] is stretched vertically by a factor of [latex]2[\/latex], shifted horizontally [latex]4[\/latex] units to the right, reflected across the horizontal axis, and then shifted vertically [latex]3[\/latex] units up.
                            \n\"Graph<\/li>\n
                          34. The graph of the function [latex]f(x)=x^3[\/latex] is compressed vertically by a factor of [latex]\\dfrac{1}{2}[\/latex].
                            \n\"Graph<\/li>\n
                          35. The graph of the function is stretched horizontally by a factor of [latex]3[\/latex] and then shifted vertically downward by [latex]3[\/latex] units.
                            \n\"Graph<\/li>\n
                          36. The graph of [latex]f(x)=\\sqrt{x}[\/latex] is shifted right [latex]4[\/latex] units and then reflected across the vertical line [latex]x=4[\/latex].
                            \n\"Graph<\/li>\n
                          37. \"Graph<\/li>\n
                          38. \"Graph<\/li>\n<\/ol>\n

                            Inverse Functions<\/span><\/h2>\n
                              \n
                            1. [latex]f^{-1}(x)=x-3[\/latex]<\/li>\n
                            2. [latex]f^{-1}(x)=2-x[\/latex]<\/li>\n
                            3. [latex]f^{-1}(x)=\\dfrac{-2x}{x-1}[\/latex]<\/li>\n
                            4. domain of [latex]f(x):[\u22127,\\infty)[\/latex]; [latex]f^{-1}(x)=\\sqrt{x}-7[\/latex]<\/li>\n
                            5. domain of [latex]f(x):[0,\\infty)[\/latex]; [latex]f^{-1}(x)=\\sqrt{x+5}[\/latex]<\/li>\n
                            6. [latex]f(g(x))=x[\/latex], [latex]g(f(x))=x[\/latex]<\/li>\n
                            7. one-to-one<\/li>\n
                            8. one-to-one<\/li>\n
                            9. not one-to-one<\/li>\n
                            10. [latex]3[\/latex]<\/li>\n
                            11. [latex]2[\/latex]<\/li>\n
                            12. \"Graph<\/li>\n
                            13. [latex][2,10][\/latex]<\/li>\n
                            14. [latex]6[\/latex]<\/li>\n
                            15. [latex]-4[\/latex]<\/li>\n
                            16. [latex]0[\/latex]<\/li>\n
                            17. [latex]1[\/latex]<\/li>\n
                            18. \n\n\n\n\n
                              [latex]x[\/latex]<\/th>\n[latex]1[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n[latex]7[\/latex]<\/td>\n[latex]12[\/latex]<\/td>\n[latex]16[\/latex]<\/td>\n<\/tr>\n
                              [latex]f^{-1}(x)[\/latex]<\/th>\n[latex]3[\/latex]<\/td>\n[latex]6[\/latex]<\/td>\n[latex]9[\/latex]<\/td>\n[latex]13[\/latex]<\/td>\n[latex]14[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                            19. [latex]f^{-1}(x)=\\dfrac{5}{9}(x-32)[\/latex]. Given the Fahrenheit temperature, [latex]x[\/latex], this formula allows you to calculate the Celsius temperature.<\/li>\n
                            20. [latex]t(d)=\\dfrac{d}{50}[\/latex], [latex]t(180)=\\dfrac{180}{50}[\/latex]. The time for the car to travel [latex]180[\/latex] miles is [latex]3.6[\/latex] hours.<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":106,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/119"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/119\/revisions"}],"predecessor-version":[{"id":127,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/119\/revisions\/127"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/106"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/119\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=119"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=119"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=119"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}