{"id":2016,"date":"2021-12-02T19:40:29","date_gmt":"2021-12-03T00:40:29","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-1\/"},"modified":"2023-09-01T15:00:11","modified_gmt":"2023-09-01T19:00:11","slug":"answer-key-11-1","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-1\/","title":{"raw":"Answer Key 11.1","rendered":"Answer Key 11.1"},"content":{"raw":"
    \r\n \t
  1. [latex]\\phantom{a}[\/latex]\r\n
      \r\n \t
    1. No<\/li>\r\n \t
    2. Yes<\/li>\r\n \t
    3. No<\/li>\r\n \t
    4. Yes<\/li>\r\n \t
    5. Yes<\/li>\r\n \t
    6. No<\/li>\r\n \t
    7. Yes<\/li>\r\n \t
    8. [latex]y^2=1+x^2[\/latex]\r\n[latex]y=\\pm \\sqrt{1+x^2}[\/latex]\r\nNo<\/li>\r\n \t
    9. [latex]\\sqrt{y}=2-x[\/latex]\r\n[latex]y=(2-x)^2[\/latex]\r\nYes<\/li>\r\n \t
    10. [latex]y^2=1-x^2[\/latex]\r\n[latex]y=\\pm \\sqrt{1-x^2}[\/latex]\r\nNo<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    11. All real numbers [latex]-\\infty, \\infty[\/latex]<\/li>\r\n \t
    12. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n5&-&4x&\\ge &0 \\\\\r\n-5&&&&-5 \\\\\r\n\\hline\r\n&&\\dfrac{-4x}{-4}&\\ge &\\dfrac{-5}{-4} \\\\ \\\\\r\n&&x&\\le &\\dfrac{5}{4} \\\\\r\n\\end{array}[\/latex][latex]\\left(-\\infty, \\dfrac{5}{4}\\right][\/latex]<\/li>\r\n \t
    13. [latex]t^2\\neq 0[\/latex]\r\n[latex]t\\neq \\sqrt{0}\\text{ or }0[\/latex]<\/li>\r\n \t
    14. All real or [latex](-\\infty, \\infty)[\/latex]<\/li>\r\n \t
    15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\nt^2&+&1&\\neq &0 \\\\\r\n&-&1&&-1 \\\\\r\n\\hline\r\n&&t^2&\\neq &-1 \\\\\r\n&&t&\\neq & i \\\\ \\\\\r\n&&t&=&\\mathbb{R}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\nx&-&16&\\ge &0 \\\\\r\n&+&16&&+16 \\\\\r\n\\hline\r\n&&x&\\ge &16 \\\\\r\n\\end{array}[\/latex]\r\n[latex][16, \\infty)[\/latex]<\/li>\r\n \t
    17. [latex]x^2-3x-4\\neq 0[\/latex]\r\n[latex](x-4)(x+1)\\neq 0[\/latex]\r\n[latex]x\\neq 4,1[\/latex]<\/li>\r\n \t
    18. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrrrr}\r\n3x&-&12&\\ge &0 \\\\\r\n&+&12&&+12 \\\\\r\n\\hline\r\n&&\\dfrac{3x}{3}&\\ge &\\dfrac{12}{3} \\\\ \\\\\r\n&&x&\\ge &4\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}[t]{rrl}\r\nx^2-25&\\neq &0 \\\\\r\n(x-5)(x+5)&\\neq &0 \\\\\r\nx&\\neq &5, -5 \\\\ \\\\\r\n\\therefore x&\\ge &4, \\neq \\pm 5\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    19. [latex]g(0)=\\cancel{4(0)}-4[\/latex]\r\n[latex]\\phantom{g(0)}=-4[\/latex]<\/li>\r\n \t
    20. [latex]g(2)=-3\\cdot 5^{-2}[\/latex]\r\n[latex]\\phantom{g(2)}=-\\dfrac{3}{25}[\/latex]<\/li>\r\n \t
    21. [latex]f(-9)=(-9)^2+4[\/latex]\r\n[latex]\\phantom{f(-9)}=81+4[\/latex]\r\n[latex]\\phantom{f(-9)}=85[\/latex]<\/li>\r\n \t
    22. [latex]f(10)=10-3[\/latex]\r\n[latex]\\phantom{f(10)}=7[\/latex]<\/li>\r\n \t
    23. [latex]f(-2)=3^{-2}-2[\/latex]\r\n[latex]\\phantom{f(-2)}=\\dfrac{1}{9}-2[\/latex]\r\n[latex]\\phantom{f(-2)}=\\dfrac{1}{9}-\\dfrac{18}{9}[\/latex]\r\n[latex]\\phantom{f(-2)}=-\\dfrac{17}{9}[\/latex]<\/li>\r\n \t
    24. [latex]f(2)=-3^{2-1}-3[\/latex]\r\n[latex]\\phantom{f(2)}=-3^1-3[\/latex]\r\n[latex]\\phantom{f(2)}=-6[\/latex]<\/li>\r\n \t
    25. [latex]k(2)=-2\\cdot 4^{2(2)-2}[\/latex]\r\n[latex]\\phantom{k(2)}=-2\\cdot 4^{4-2}[\/latex]\r\n[latex]\\phantom{k(2)}=-2\\cdot 4^2[\/latex]\r\n[latex]\\phantom{k(2)}=-32[\/latex]<\/li>\r\n \t
    26. [latex]p(-2)=-2\\cdot 4^{2(-2)+1}+1[\/latex]\r\n[latex]\\phantom{p(-2)}=-2\\cdot 4^{-4+1}+1[\/latex]\r\n[latex]\\phantom{p(-2)}=-2\\cdot 4^{-3}+1 [\/latex]\r\n[latex]\\phantom{p(-2)}=-\\dfrac{2}{64}+1[\/latex]\r\n[latex]\\phantom{p(-2)}=-\\dfrac{1}{32}+1 \\Rightarrow \\dfrac{-31}{32}[\/latex]<\/li>\r\n \t
    27. [latex]h(-4x)=(-4x)^3+2[\/latex]\r\n[latex]\\phantom{h(-4x)}=-64x^3+2[\/latex]<\/li>\r\n \t
    28. [latex]h(n+2)=4(n+2)+2[\/latex]\r\n[latex]\\phantom{h(n+2)}=4n+8+2[\/latex]\r\n[latex]\\phantom{h(n+2)}=4n+10[\/latex]<\/li>\r\n \t
    29. [latex]h(-1+x)=3(-1+x)+2[\/latex]\r\n[latex]\\phantom{h(-1+x)}=-3+3x+2 [\/latex]\r\n[latex]\\phantom{h(-1+x)}=3x-1[\/latex]<\/li>\r\n \t
    30. [latex]h(\\dfrac{1}{3})=-3\\cdot 2^{\\frac{1}{3}+3}[\/latex]\r\n[latex]\\phantom{h(\\dfrac{1}{3})}= -2^3\\cdot 3\\sqrt[3]{2}[\/latex]\r\n[latex]\\phantom{h(\\dfrac{1}{3})}=-8\\cdot 3\\sqrt[3]{2}[\/latex]\r\n[latex]\\phantom{h(\\dfrac{1}{3})}=-24 \\sqrt[3]{2}[\/latex]<\/li>\r\n \t
    31. [latex]h(x^4)=(x^4)^2+1[\/latex]\r\n[latex]\\phantom{h(x^4)}=x^8+1[\/latex]<\/li>\r\n \t
    32. [latex]h(t^2)=(t^2)^2+t [\/latex]\r\n[latex]\\phantom{h(t^2)}=t^4+t[\/latex]<\/li>\r\n \t
    33. [latex]f(0)=|\\cancel{3(0)}+1|+1[\/latex]\r\n[latex]\\phantom{f(0)}=1+1\\text{ or }2[\/latex]<\/li>\r\n \t
    34. [latex]f(-6)=-2 |-(-6)-2 | +1 [\/latex]\r\n[latex]\\phantom{f(-6)}=-2 |6-2| + 1[\/latex]\r\n[latex]\\phantom{f(-6)}=-2(4)+1[\/latex]\r\n[latex]\\phantom{f(-6)}=-8 + 1\\text{ or }-7[\/latex]<\/li>\r\n \t
    35. [latex]f(10)=|10+3| [\/latex]\r\n[latex]\\phantom{f(10)}=13[\/latex]<\/li>\r\n \t
    36. [latex]p(5)=-|5|+1 [\/latex]\r\n[latex]\\phantom{p(-5)}=-5+1[\/latex]\r\n[latex]\\phantom{p(-5)}=-4[\/latex]<\/li>\r\n<\/ol>","rendered":"
        \n
      1. [latex]\\phantom{a}[\/latex]\n
          \n
        1. No<\/li>\n
        2. Yes<\/li>\n
        3. No<\/li>\n
        4. Yes<\/li>\n
        5. Yes<\/li>\n
        6. No<\/li>\n
        7. Yes<\/li>\n
        8. [latex]y^2=1+x^2[\/latex]
          \n[latex]y=\\pm \\sqrt{1+x^2}[\/latex]
          \nNo<\/li>\n
        9. [latex]\\sqrt{y}=2-x[\/latex]
          \n[latex]y=(2-x)^2[\/latex]
          \nYes<\/li>\n
        10. [latex]y^2=1-x^2[\/latex]
          \n[latex]y=\\pm \\sqrt{1-x^2}[\/latex]
          \nNo<\/li>\n<\/ol>\n<\/li>\n
        11. All real numbers [latex]-\\infty, \\infty[\/latex]<\/li>\n
        12. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrr} 5&-&4x&\\ge &0 \\\\ -5&&&&-5 \\\\ \\hline &&\\dfrac{-4x}{-4}&\\ge &\\dfrac{-5}{-4} \\\\ \\\\ &&x&\\le &\\dfrac{5}{4} \\\\ \\end{array}[\/latex][latex]\\left(-\\infty, \\dfrac{5}{4}\\right][\/latex]<\/li>\n
        13. [latex]t^2\\neq 0[\/latex]
          \n[latex]t\\neq \\sqrt{0}\\text{ or }0[\/latex]<\/li>\n
        14. All real or [latex](-\\infty, \\infty)[\/latex]<\/li>\n
        15. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrr} t^2&+&1&\\neq &0 \\\\ &-&1&&-1 \\\\ \\hline &&t^2&\\neq &-1 \\\\ &&t&\\neq & i \\\\ \\\\ &&t&=&\\mathbb{R} \\end{array}[\/latex]<\/li>\n
        16. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrr} x&-&16&\\ge &0 \\\\ &+&16&&+16 \\\\ \\hline &&x&\\ge &16 \\\\ \\end{array}[\/latex]
          \n[latex][16, \\infty)[\/latex]<\/li>\n
        17. [latex]x^2-3x-4\\neq 0[\/latex]
          \n[latex](x-4)(x+1)\\neq 0[\/latex]
          \n[latex]x\\neq 4,1[\/latex]<\/li>\n
        18. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrr} 3x&-&12&\\ge &0 \\\\ &+&12&&+12 \\\\ \\hline &&\\dfrac{3x}{3}&\\ge &\\dfrac{12}{3} \\\\ \\\\ &&x&\\ge &4 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} x^2-25&\\neq &0 \\\\ (x-5)(x+5)&\\neq &0 \\\\ x&\\neq &5, -5 \\\\ \\\\ \\therefore x&\\ge &4, \\neq \\pm 5 \\end{array} \\end{array}[\/latex]<\/li>\n
        19. [latex]g(0)=\\cancel{4(0)}-4[\/latex]
          \n[latex]\\phantom{g(0)}=-4[\/latex]<\/li>\n
        20. [latex]g(2)=-3\\cdot 5^{-2}[\/latex]
          \n[latex]\\phantom{g(2)}=-\\dfrac{3}{25}[\/latex]<\/li>\n
        21. [latex]f(-9)=(-9)^2+4[\/latex]
          \n[latex]\\phantom{f(-9)}=81+4[\/latex]
          \n[latex]\\phantom{f(-9)}=85[\/latex]<\/li>\n
        22. [latex]f(10)=10-3[\/latex]
          \n[latex]\\phantom{f(10)}=7[\/latex]<\/li>\n
        23. [latex]f(-2)=3^{-2}-2[\/latex]
          \n[latex]\\phantom{f(-2)}=\\dfrac{1}{9}-2[\/latex]
          \n[latex]\\phantom{f(-2)}=\\dfrac{1}{9}-\\dfrac{18}{9}[\/latex]
          \n[latex]\\phantom{f(-2)}=-\\dfrac{17}{9}[\/latex]<\/li>\n
        24. [latex]f(2)=-3^{2-1}-3[\/latex]
          \n[latex]\\phantom{f(2)}=-3^1-3[\/latex]
          \n[latex]\\phantom{f(2)}=-6[\/latex]<\/li>\n
        25. [latex]k(2)=-2\\cdot 4^{2(2)-2}[\/latex]
          \n[latex]\\phantom{k(2)}=-2\\cdot 4^{4-2}[\/latex]
          \n[latex]\\phantom{k(2)}=-2\\cdot 4^2[\/latex]
          \n[latex]\\phantom{k(2)}=-32[\/latex]<\/li>\n
        26. [latex]p(-2)=-2\\cdot 4^{2(-2)+1}+1[\/latex]
          \n[latex]\\phantom{p(-2)}=-2\\cdot 4^{-4+1}+1[\/latex]
          \n[latex]\\phantom{p(-2)}=-2\\cdot 4^{-3}+1[\/latex]
          \n[latex]\\phantom{p(-2)}=-\\dfrac{2}{64}+1[\/latex]
          \n[latex]\\phantom{p(-2)}=-\\dfrac{1}{32}+1 \\Rightarrow \\dfrac{-31}{32}[\/latex]<\/li>\n
        27. [latex]h(-4x)=(-4x)^3+2[\/latex]
          \n[latex]\\phantom{h(-4x)}=-64x^3+2[\/latex]<\/li>\n
        28. [latex]h(n+2)=4(n+2)+2[\/latex]
          \n[latex]\\phantom{h(n+2)}=4n+8+2[\/latex]
          \n[latex]\\phantom{h(n+2)}=4n+10[\/latex]<\/li>\n
        29. [latex]h(-1+x)=3(-1+x)+2[\/latex]
          \n[latex]\\phantom{h(-1+x)}=-3+3x+2[\/latex]
          \n[latex]\\phantom{h(-1+x)}=3x-1[\/latex]<\/li>\n
        30. [latex]h(\\dfrac{1}{3})=-3\\cdot 2^{\\frac{1}{3}+3}[\/latex]
          \n[latex]\\phantom{h(\\dfrac{1}{3})}= -2^3\\cdot 3\\sqrt[3]{2}[\/latex]
          \n[latex]\\phantom{h(\\dfrac{1}{3})}=-8\\cdot 3\\sqrt[3]{2}[\/latex]
          \n[latex]\\phantom{h(\\dfrac{1}{3})}=-24 \\sqrt[3]{2}[\/latex]<\/li>\n
        31. [latex]h(x^4)=(x^4)^2+1[\/latex]
          \n[latex]\\phantom{h(x^4)}=x^8+1[\/latex]<\/li>\n
        32. [latex]h(t^2)=(t^2)^2+t[\/latex]
          \n[latex]\\phantom{h(t^2)}=t^4+t[\/latex]<\/li>\n
        33. [latex]f(0)=|\\cancel{3(0)}+1|+1[\/latex]
          \n[latex]\\phantom{f(0)}=1+1\\text{ or }2[\/latex]<\/li>\n
        34. [latex]f(-6)=-2 |-(-6)-2 | +1[\/latex]
          \n[latex]\\phantom{f(-6)}=-2 |6-2| + 1[\/latex]
          \n[latex]\\phantom{f(-6)}=-2(4)+1[\/latex]
          \n[latex]\\phantom{f(-6)}=-8 + 1\\text{ or }-7[\/latex]<\/li>\n
        35. [latex]f(10)=|10+3|[\/latex]
          \n[latex]\\phantom{f(10)}=13[\/latex]<\/li>\n
        36. [latex]p(5)=-|5|+1[\/latex]
          \n[latex]\\phantom{p(-5)}=-5+1[\/latex]
          \n[latex]\\phantom{p(-5)}=-4[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":107,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2016","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2016","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2016\/revisions"}],"predecessor-version":[{"id":2238,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2016\/revisions\/2238"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2016\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2016"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2016"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2016"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}