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Graphs of Factor= able Polynomials
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0315.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
We start = with the graphs of the polynomials y =3D ±xN.
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Graphs of Factor= able Polynomials
We start = with the graphs of the polynomials y =3D ±xN.
The graph= s y =3D x
y =3D x
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Graphs of Factor= able Polynomials
The graph= s y =3D x
y =3D x
y =3D x
(1, 1)
(-1, 1)
We start = with the graphs of the polynomials y =3D ±xN.
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Graphs of Factor= able Polynomials
The graph= s y =3D x
y =3D x
y =3D x
y =3D x
y =3D -x
y =3D -x
y =3D -x
(1, 1)
(-1, 1)
(-1,-1)
(1,-1)
We start = with the graphs of the polynomials y =3D ±xN.
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R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAkAgQAAAAAAALvg4wECAwITBIJoJ93BnENyhvoupjvOlShAAQA7 ------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0245.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
The graph= s y =3D x
y =3D x
y =3D x
y =3D x
y =3D -x
y =3D -x
y =3D -x
y =3D ±xeven:
y =3D xeven
y =3D -xeven
(1, 1)
(-1, 1)
(-1,-1)
(1,-1)
We start = with the graphs of the polynomials y =3D ±xN.
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file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0247.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
y =3D x
y =3D x
(1, 1)
(-1, -1)
The graph= s y =3D x
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Graphs of Factor= able Polynomials
y =3D x
y =3D x
y =3D x
(1, 1)
(-1, -1)
The graph= s y =3D x
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Graphs of Factor= able Polynomials
The graph= s y =3D x
y =3D x
y =3D x
y =3D x
y =3D -x
y =3D -x
y =3D -x
(1, 1)
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Graphs of Factor= able Polynomials
The graph= s y =3D x
y =3D x
y =3D x
y =3D x
y =3D -x
y =3D -x
y =3D -x
y =3D ±xodd:
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(1, 1)
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base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAALvg4wECAwIWBIJhFuKCzptovmphy9j2y2zackRGAQA7 ------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0250_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAALvg4wECAwIVBIJoFuIe2JuxzYcutjp3eUVMogAFADs= ------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0250_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAALvg4wECAwIYhINhF+KiznuqTVcvtRppKF2Rh0VLsgAFADs= ------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0250_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAALvg4wECAwIVBIJoFuIe2JuxzYcutjp3eUVMogAFADs= ------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0253.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0264.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0265.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0266.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0267.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms. =
For large |x|, the leading term anx dominates the = lower degree terms.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0268.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms. =
For large |x|, the leading term anx dominates the lower degree terms. For x's such that | x | are large, the "lower degree terms" is negligible compare to anx.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0269.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms. =
For large |x|, the leading term anx dominates the lower degree terms. For x's such that | x | are large, the "lower degree terms" is negligible compare to anx.
Hence, for x where |x| is "large", the graph of P(x) resembles the graph y =3D anxn<= span lang=3DEN-US style=3D'mso-bidi-font-family:Arial;mso-hansi-font-family:Ari= al; font-size:156%;mso-fareast-language:ZH-CN'>.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0270.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms. =
For large |x|, the leading term anx dominates the lower degree terms. For x's such that | x | are large, the "lower degree terms" is negligible compare to anx.
Hence, for x where |x| is "large", the graph of P(x) resembles the graph y =3D anxn<= span lang=3DEN-US style=3D'mso-bidi-font-family:Arial;mso-hansi-font-family:Ari= al; font-size:156%;mso-fareast-language:ZH-CN'>.
This means there're four behaviors of
polynomial-graphs to the far left or far right
(as | x | becomes large).
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0271.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
Facts abo= ut the graphs of polynomials:
• The graphs of polynomials are unbroken curves.
• Polynomial curves= are smooth (no corners).
• Let P(x) =3D anx + lower degree terms. =
For large |x|, the leading term anx dominates the lower degree terms. For x's such that | x | are large, the "lower degree terms" is negligible compare to anx.
Hence, for x where |x| is "large", the graph of P(x) resembles the graph y =3D anxn<= span lang=3DEN-US style=3D'mso-bidi-font-family:Arial;mso-hansi-font-family:Ari= al; font-size:156%;mso-fareast-language:ZH-CN'>.
This means there're four behaviors of
polynomial-graphs to the far left or far right
(as | x | becomes large). These behaviors are based on = the sign the leading term anxn, and whether n is <= span lang=3DEN-US style=3D'mso-bidi-font-family:Arial;mso-hansi-font-family:Ari= al; font-size:156%;mso-fareast-language:ZH-CN'>even or odd.
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0275.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
This behaviors of polynomial-gr= aphs to the "sides":
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0251.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities
Graphs of Factor= able Polynomials
y =3D +xeven + lower degree terms: &= #13;
This behaviors of polynomial-gr= aphs to the "sides":
------=_NextPart_01C82E62.9E1E2EB0 Content-Location: file:///C:/650611F3/5GraphsofFactorablePolynomials_files/slide0251_image079.jpg Content-Transfer-Encoding: base64 Content-Type: image/jpeg /9j/4AAQSkZJRgABAQEANQA1AAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIf IiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7 Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACGAI8DASIA AhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQA AAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3 ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWm p6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEA AwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSEx BhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElK U1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3 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Graphs of Factor= able Polynomials
y =3D +xeven + lower degree terms: &= #13;
y =3D –xeven + lower degree terms: &= #13;
This behaviors of polynomial-gr= aphs to the "sides":
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Graphs of Factor= able Polynomials
y =3D +xeven + lower degree terms: &= #13;
y =3D –xeven + lower degree terms: &= #13;
This behaviors of polynomial-gr= aphs to the "sides":
y =3D +xodd + lower degree terms: &= #13;
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Graphs of Factor= able Polynomials
y =3D +xeven + lower degree terms: &= #13;
y =3D –xeven + lower degree terms: &= #13;
This behaviors of polynomial-gr= aphs to the "sides":
y =3D +xodd + lower degree terms: &= #13;
y =3D –xodd + lower degree terms: &= #13;
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