{"id":118,"date":"2026-01-12T15:48:55","date_gmt":"2026-01-12T15:48:55","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=118"},"modified":"2026-01-12T15:48:55","modified_gmt":"2026-01-12T15:48:55","slug":"function-basic-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/function-basic-get-stronger-answer-key\/","title":{"raw":"Function Basic: Get Stronger Answer Key","rendered":"Function Basic: Get Stronger Answer Key"},"content":{"raw":"

Introduction to Functions<\/span><\/h2>\r\n
    \r\n \t
  1. function<\/li>\r\n \t
  2. function<\/li>\r\n \t
  3. function<\/li>\r\n \t
  4. function<\/li>\r\n \t
  5. function<\/li>\r\n \t
  6. function<\/li>\r\n \t
  7. function<\/li>\r\n \t
  8. function<\/li>\r\n \t
  9. not a function<\/li>\r\n \t
  10. [latex]f(-3)=-11[\/latex];\r\n[latex]f(2)=-1[\/latex];\r\n[latex]f(-a)=-2a-5[\/latex];\r\n[latex]-f(a)=-2a+5[\/latex];\r\n[latex]f(a+h)=2a+2h-5[\/latex]<\/li>\r\n \t
  11. [latex]f(-3)=\\sqrt{5}+5[\/latex];\r\n[latex]f(2)=5[\/latex];\r\n[latex]f(-a)=\\sqrt{2+a}+5[\/latex];\r\n[latex]-f(a)=-\\sqrt{2-a}-5[\/latex];\r\n[latex]f(a+h)=\\sqrt{2-a-h}+5[\/latex]<\/li>\r\n \t
  12. [latex]f(-3)=2[\/latex];\r\n[latex]f(2)=1-3=-2[\/latex];\r\n[latex]f(-a)=|-a-1|-|-a+1|[\/latex];\r\n[latex]-f(a)=-|a-1|+|a+1|[\/latex];\r\n[latex]f(a+h)=|a+h-1|-|a+h+1|[\/latex]<\/li>\r\n \t
  13. [latex]\\dfrac{g(x)-g(a)}{x-a}=x+a+2[\/latex], [latex]x\\neq a[\/latex]<\/li>\r\n \t
  14. \r\n
      \r\n \t
    1. [latex]f(-2)=14[\/latex]<\/li>\r\n \t
    2. [latex]x=3[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    3. \r\n
        \r\n \t
      1. [latex]f(5)=10[\/latex]<\/li>\r\n \t
      2. [latex]x=-1[\/latex] or [latex]x=4[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      3. \r\n
          \r\n \t
        1. [latex]f(t)=6-\\dfrac{2}{3}t[\/latex]<\/li>\r\n \t
        2. [latex]f(-3)=8[\/latex]<\/li>\r\n \t
        3. [latex]t=6[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
        4. not a function<\/li>\r\n \t
        5. function<\/li>\r\n \t
        6. function<\/li>\r\n \t
        7. function<\/li>\r\n \t
        8. function<\/li>\r\n \t
        9. function<\/li>\r\n \t
        10. \r\n
            \r\n \t
          1. [latex]f(0)=1[\/latex]<\/li>\r\n \t
          2. [latex]f(x)=-3[\/latex], [latex]x=-2[\/latex] or [latex]x=2[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
          3. not a function so it is also not a one-to-one function<\/li>\r\n \t
          4. one-to-one function<\/li>\r\n \t
          5. function, but not one-to-one<\/li>\r\n \t
          6. function<\/li>\r\n \t
          7. function<\/li>\r\n \t
          8. not a function<\/li>\r\n \t
          9. [latex]f(x)=1[\/latex], [latex]x=2[\/latex]<\/li>\r\n \t
          10. \r\n
              \r\n \t
            1. [latex]g(5000)=50[\/latex]<\/li>\r\n \t
            2. The number of cubic yards of dirt required for a garden of [latex]100[\/latex] square feet is [latex]1[\/latex].<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            3. \r\n
                \r\n \t
              1. The height of a rocket above ground after [latex]1[\/latex] second is [latex]200[\/latex] ft.<\/li>\r\n \t
              2. The height of a rocket above ground after [latex]2[\/latex] seconds is [latex]350[\/latex] ft.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                Domain and Range<\/span><\/h2>\r\n
                  \r\n \t
                1. [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
                2. [latex](-\\infty,3][\/latex]<\/li>\r\n \t
                3. [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
                4. [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
                5. [latex](-\\infty,-\\dfrac{1}{2})\\cup(-\\dfrac{1}{2},\\infty)[\/latex]<\/li>\r\n \t
                6. [latex](-\\infty,-11)\\cup(-11,2)\\cup(2,\\infty)[\/latex]<\/li>\r\n \t
                7. [latex](-\\infty,-3)\\cup(-3,5)\\cup(5,\\infty)[\/latex]<\/li>\r\n \t
                8. [latex](-\\infty,5)[\/latex]<\/li>\r\n \t
                9. [latex][6,\\infty)[\/latex]<\/li>\r\n \t
                10. [latex](-\\infty,-9)\\cup(-9,9)\\cup(9,\\infty)[\/latex]<\/li>\r\n \t
                11. domain: [latex][2,8][\/latex], range: [latex][6,8][\/latex]<\/li>\r\n \t
                12. domain: [latex][-4,4][\/latex], range: [latex][0,2][\/latex]<\/li>\r\n \t
                13. domain: [latex][-5,3)[\/latex], range: [latex][0,2][\/latex]<\/li>\r\n \t
                14. domain: [latex](-\\infty,1][\/latex], range: [latex][0,\\infty)[\/latex]<\/li>\r\n \t
                15. domain: [latex][-6,-\\dfrac{1}{6}]\\cup[\\dfrac{1}{6},6][\/latex]; range: [latex][-6,-\\dfrac{1}{6}]\\cup[\\dfrac{1}{6},6][\/latex]<\/li>\r\n \t
                16. domain: [latex][-3,\\infty)[\/latex]; range: [latex][0,\\infty)[\/latex]<\/li>\r\n \t
                17. domain: [latex](-\\infty,\\infty)[\/latex]\r\n\"Graph<\/li>\r\n \t
                18. domain: [latex](-\\infty,\\infty)[\/latex]\r\n\"Graph<\/li>\r\n \t
                19. domain: [latex](-\\infty,\\infty)[\/latex]\r\n\"Graph<\/li>\r\n \t
                20. domain: [latex](-\\infty,\\infty)[\/latex]\r\n\"Graph<\/li>\r\n \t
                21. [latex]f(-3)=1[\/latex]; [latex]f(-2)=0[\/latex]; [latex]f(-1)=0[\/latex]; [latex]f(0)=0[\/latex]<\/li>\r\n \t
                22. [latex]f(-1)=-4[\/latex]; [latex]f(0)=6[\/latex]; [latex]f(2)=20[\/latex]; [latex]f(4)=34[\/latex]<\/li>\r\n \t
                23. [latex]f(-1)=-5[\/latex]; [latex]f(0)=3[\/latex]; [latex]f(2)=3[\/latex]; [latex]f(4)=16[\/latex]<\/li>\r\n \t
                24. domain: [latex](-\\infty,1)\\cup(1,\\infty)[\/latex]<\/li>\r\n<\/ol>\r\n

                  Rates of Change and Behavior of Graphs<\/span><\/h2>\r\n
                    \r\n \t
                  1. [latex]4x+2h[\/latex]<\/li>\r\n \t
                  2. [latex]\\dfrac{-1}{13(13+h)}[\/latex]<\/li>\r\n \t
                  3. [latex]3h^2+9h+9[\/latex]<\/li>\r\n \t
                  4. [latex]4x+2h-3[\/latex]<\/li>\r\n \t
                  5. [latex]\\dfrac{4}{3}[\/latex]<\/li>\r\n \t
                  6. increasing on [latex](-\\infty,-2.5)\\cup(1,\\infty)[\/latex], decreasing on [latex](-2.5,1)[\/latex]<\/li>\r\n \t
                  7. increasing on [latex](-\\infty,1)\\cup(3,4)[\/latex], decreasing on [latex](1,3)\\cup(4,\\infty)[\/latex]<\/li>\r\n \t
                  8. [latex]-4[\/latex]<\/li>\r\n \t
                  9. [latex]27[\/latex]<\/li>\r\n \t
                  10. [latex]-0.167[\/latex]<\/li>\r\n \t
                  11. [latex]2.7[\/latex] gallons per minute<\/li>\r\n \t
                  12. approximately [latex]-0.6[\/latex] milligrams per day<\/li>\r\n<\/ol>","rendered":"

                    Introduction to Functions<\/span><\/h2>\n
                      \n
                    1. function<\/li>\n
                    2. function<\/li>\n
                    3. function<\/li>\n
                    4. function<\/li>\n
                    5. function<\/li>\n
                    6. function<\/li>\n
                    7. function<\/li>\n
                    8. function<\/li>\n
                    9. not a function<\/li>\n
                    10. [latex]f(-3)=-11[\/latex];
                      \n[latex]f(2)=-1[\/latex];
                      \n[latex]f(-a)=-2a-5[\/latex];
                      \n[latex]-f(a)=-2a+5[\/latex];
                      \n[latex]f(a+h)=2a+2h-5[\/latex]<\/li>\n
                    11. [latex]f(-3)=\\sqrt{5}+5[\/latex];
                      \n[latex]f(2)=5[\/latex];
                      \n[latex]f(-a)=\\sqrt{2+a}+5[\/latex];
                      \n[latex]-f(a)=-\\sqrt{2-a}-5[\/latex];
                      \n[latex]f(a+h)=\\sqrt{2-a-h}+5[\/latex]<\/li>\n
                    12. [latex]f(-3)=2[\/latex];
                      \n[latex]f(2)=1-3=-2[\/latex];
                      \n[latex]f(-a)=|-a-1|-|-a+1|[\/latex];
                      \n[latex]-f(a)=-|a-1|+|a+1|[\/latex];
                      \n[latex]f(a+h)=|a+h-1|-|a+h+1|[\/latex]<\/li>\n
                    13. [latex]\\dfrac{g(x)-g(a)}{x-a}=x+a+2[\/latex], [latex]x\\neq a[\/latex]<\/li>\n
                    14. \n
                        \n
                      1. [latex]f(-2)=14[\/latex]<\/li>\n
                      2. [latex]x=3[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                      3. \n
                          \n
                        1. [latex]f(5)=10[\/latex]<\/li>\n
                        2. [latex]x=-1[\/latex] or [latex]x=4[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                        3. \n
                            \n
                          1. [latex]f(t)=6-\\dfrac{2}{3}t[\/latex]<\/li>\n
                          2. [latex]f(-3)=8[\/latex]<\/li>\n
                          3. [latex]t=6[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                          4. not a function<\/li>\n
                          5. function<\/li>\n
                          6. function<\/li>\n
                          7. function<\/li>\n
                          8. function<\/li>\n
                          9. function<\/li>\n
                          10. \n
                              \n
                            1. [latex]f(0)=1[\/latex]<\/li>\n
                            2. [latex]f(x)=-3[\/latex], [latex]x=-2[\/latex] or [latex]x=2[\/latex]<\/li>\n<\/ol>\n<\/li>\n
                            3. not a function so it is also not a one-to-one function<\/li>\n
                            4. one-to-one function<\/li>\n
                            5. function, but not one-to-one<\/li>\n
                            6. function<\/li>\n
                            7. function<\/li>\n
                            8. not a function<\/li>\n
                            9. [latex]f(x)=1[\/latex], [latex]x=2[\/latex]<\/li>\n
                            10. \n
                                \n
                              1. [latex]g(5000)=50[\/latex]<\/li>\n
                              2. The number of cubic yards of dirt required for a garden of [latex]100[\/latex] square feet is [latex]1[\/latex].<\/li>\n<\/ol>\n<\/li>\n
                              3. \n
                                  \n
                                1. The height of a rocket above ground after [latex]1[\/latex] second is [latex]200[\/latex] ft.<\/li>\n
                                2. The height of a rocket above ground after [latex]2[\/latex] seconds is [latex]350[\/latex] ft.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                  Domain and Range<\/span><\/h2>\n
                                    \n
                                  1. [latex](-\\infty,\\infty)[\/latex]<\/li>\n
                                  2. [latex](-\\infty,3][\/latex]<\/li>\n
                                  3. [latex](-\\infty,\\infty)[\/latex]<\/li>\n
                                  4. [latex](-\\infty,\\infty)[\/latex]<\/li>\n
                                  5. [latex](-\\infty,-\\dfrac{1}{2})\\cup(-\\dfrac{1}{2},\\infty)[\/latex]<\/li>\n
                                  6. [latex](-\\infty,-11)\\cup(-11,2)\\cup(2,\\infty)[\/latex]<\/li>\n
                                  7. [latex](-\\infty,-3)\\cup(-3,5)\\cup(5,\\infty)[\/latex]<\/li>\n
                                  8. [latex](-\\infty,5)[\/latex]<\/li>\n
                                  9. [latex][6,\\infty)[\/latex]<\/li>\n
                                  10. [latex](-\\infty,-9)\\cup(-9,9)\\cup(9,\\infty)[\/latex]<\/li>\n
                                  11. domain: [latex][2,8][\/latex], range: [latex][6,8][\/latex]<\/li>\n
                                  12. domain: [latex][-4,4][\/latex], range: [latex][0,2][\/latex]<\/li>\n
                                  13. domain: [latex][-5,3)[\/latex], range: [latex][0,2][\/latex]<\/li>\n
                                  14. domain: [latex](-\\infty,1][\/latex], range: [latex][0,\\infty)[\/latex]<\/li>\n
                                  15. domain: [latex][-6,-\\dfrac{1}{6}]\\cup[\\dfrac{1}{6},6][\/latex]; range: [latex][-6,-\\dfrac{1}{6}]\\cup[\\dfrac{1}{6},6][\/latex]<\/li>\n
                                  16. domain: [latex][-3,\\infty)[\/latex]; range: [latex][0,\\infty)[\/latex]<\/li>\n
                                  17. domain: [latex](-\\infty,\\infty)[\/latex]
                                    \n\"Graph<\/li>\n
                                  18. domain: [latex](-\\infty,\\infty)[\/latex]
                                    \n\"Graph<\/li>\n
                                  19. domain: [latex](-\\infty,\\infty)[\/latex]
                                    \n\"Graph<\/li>\n
                                  20. domain: [latex](-\\infty,\\infty)[\/latex]
                                    \n\"Graph<\/li>\n
                                  21. [latex]f(-3)=1[\/latex]; [latex]f(-2)=0[\/latex]; [latex]f(-1)=0[\/latex]; [latex]f(0)=0[\/latex]<\/li>\n
                                  22. [latex]f(-1)=-4[\/latex]; [latex]f(0)=6[\/latex]; [latex]f(2)=20[\/latex]; [latex]f(4)=34[\/latex]<\/li>\n
                                  23. [latex]f(-1)=-5[\/latex]; [latex]f(0)=3[\/latex]; [latex]f(2)=3[\/latex]; [latex]f(4)=16[\/latex]<\/li>\n
                                  24. domain: [latex](-\\infty,1)\\cup(1,\\infty)[\/latex]<\/li>\n<\/ol>\n

                                    Rates of Change and Behavior of Graphs<\/span><\/h2>\n
                                      \n
                                    1. [latex]4x+2h[\/latex]<\/li>\n
                                    2. [latex]\\dfrac{-1}{13(13+h)}[\/latex]<\/li>\n
                                    3. [latex]3h^2+9h+9[\/latex]<\/li>\n
                                    4. [latex]4x+2h-3[\/latex]<\/li>\n
                                    5. [latex]\\dfrac{4}{3}[\/latex]<\/li>\n
                                    6. increasing on [latex](-\\infty,-2.5)\\cup(1,\\infty)[\/latex], decreasing on [latex](-2.5,1)[\/latex]<\/li>\n
                                    7. increasing on [latex](-\\infty,1)\\cup(3,4)[\/latex], decreasing on [latex](1,3)\\cup(4,\\infty)[\/latex]<\/li>\n
                                    8. [latex]-4[\/latex]<\/li>\n
                                    9. [latex]27[\/latex]<\/li>\n
                                    10. [latex]-0.167[\/latex]<\/li>\n
                                    11. [latex]2.7[\/latex] gallons per minute<\/li>\n
                                    12. approximately [latex]-0.6[\/latex] milligrams per day<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":5,"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\/118"}],"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\/118\/revisions"}],"predecessor-version":[{"id":126,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/118\/revisions\/126"}],"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\/118\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=118"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=118"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=118"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}