All polynomial functions{{CMD_108}}, meaning functions of the form {{MATH_109}} where {{MATH_110}} is a positive integer and each coefficient {{MATH_111}}, {{MATH_112}}, is a real number, are {{CMD_113}}continuous for all real numbers{{CMD_114}}. {{CMD_115}} In order to show that any polynomial, {{MATH_116}}, is continuous at any real number, {{MATH_117}}, we have to show that {{MATH_118}} Write with me: {{MATH_119}} Now by the Sum Law, {{MATH_120}} and by the Product Law, {{ENV_121}} and by Continuity {{MATH_122}} And this equals{{CMD_123}} {{MATH_124}} Since we have shown that {{MATH_125}}, we have shown that {{MATH_126}} is continuous at {{MATH_127}}. {{CMD_128}} {{CMD_129}}