{"id":1294,"date":"2015-11-12T18:35:30","date_gmt":"2015-11-12T18:35:30","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=1294"},"modified":"2015-11-12T18:35:30","modified_gmt":"2015-11-12T18:35:30","slug":"recognize-characteristics-of-graphs-of-polynomial-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/recognize-characteristics-of-graphs-of-polynomial-functions\/","title":{"raw":"Recognize characteristics of graphs of polynomial functions","rendered":"Recognize characteristics of graphs of polynomial functions"},"content":{"raw":"

Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous. Figure 1 shows\u00a0a graph that represents a polynomial function<\/strong> and a graph that represents a function that is not a polynomial.\n<\/span><\/p>\n\n\n[caption id=\"\" align=\"aligncenter\" width=\"900\"]\"GraphFigure 1<\/b>[\/caption]\n\n

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Example 1: Recognizing Polynomial Functions<\/h3>\nWhich of the graphs in Figure 2\u00a0represents a polynomial function?\n<\/span>\n\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]\"TwoFigure 2<\/b>[\/caption]\n\n<\/div>\n
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Solution<\/h3>\n

The graphs of f<\/em>\u00a0and h<\/em>\u00a0are graphs of polynomial functions. They are smooth and continuous<\/strong>.<\/p>\n

The graphs of g<\/em>\u00a0and k\u00a0<\/em>are graphs of functions that are not polynomials. The graph of function g<\/em>\u00a0has a sharp corner. The graph of function k<\/em>\u00a0is not continuous.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n

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Q & A<\/h3>\n

Do all polynomial functions have as their domain all real numbers?<\/strong><\/p>\n

Yes. Any real number is a valid input for a polynomial function.<\/em><\/p>\n\n<\/div>","rendered":"

Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous. Figure 1 shows\u00a0a graph that represents a polynomial function<\/strong> and a graph that represents a function that is not a polynomial.
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\"Graph<\/p>\n

Figure 1<\/b><\/p>\n<\/div>\n

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Example 1: Recognizing Polynomial Functions<\/h3>\n

Which of the graphs in Figure 2\u00a0represents a polynomial function?
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\"Two<\/p>\n

Figure 2<\/b><\/p>\n<\/div>\n<\/div>\n

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Solution<\/h3>\n

The graphs of f<\/em>\u00a0and h<\/em>\u00a0are graphs of polynomial functions. They are smooth and continuous<\/strong>.<\/p>\n

The graphs of g<\/em>\u00a0and k\u00a0<\/em>are graphs of functions that are not polynomials. The graph of function g<\/em>\u00a0has a sharp corner. The graph of function k<\/em>\u00a0is not continuous.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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Q & A<\/h3>\n

Do all polynomial functions have as their domain all real numbers?<\/strong><\/p>\n

Yes. Any real number is a valid input for a polynomial function.<\/em><\/p>\n<\/div>\n\n\t\t\t

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