{"id":16028,"date":"2019-09-26T17:24:04","date_gmt":"2019-09-26T17:24:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-piecewise-defined-linear-functions\/"},"modified":"2024-05-02T15:55:32","modified_gmt":"2024-05-02T15:55:32","slug":"outcome-piecewise-defined-linear-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-piecewise-defined-linear-functions\/","title":{"raw":"Introduction to Piecewise Functions","rendered":"Introduction to Piecewise Functions"},"content":{"raw":"Some functions come in pieces. In this section, we will learn about how to define and graph functions that are essentially collections of discrete pieces. Examples of something defined this way include designing the profile of a car, figuring out your mobile phone plan, and calculating\u00a0income tax rates. For example, your tax rate depends on your income and is the same for a range of incomes as shown in the table below:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Marginal Tax Rate<\/th>\r\nSingle Taxable Income<\/th>\r\nMarried Filing Jointly or Qualified Widow(er) Taxable Income<\/th>\r\nMarried Filing Separately Taxable Income<\/th>\r\nHead of Household Taxable Income<\/th>\r\n<\/tr>\r\n
10%<\/th>\r\n[latex]$0 \u2013 $9,275[\/latex]<\/td>\r\n[latex]$0 \u2013 $18,550[\/latex]<\/td>\r\n[latex]$0 \u2013 $9,275[\/latex]<\/td>\r\n[latex]$0 \u2013 $13,250[\/latex]<\/td>\r\n<\/tr>\r\n
15%<\/th>\r\n[latex]$9,276 \u2013 $37,650[\/latex]<\/td>\r\n[latex]$18,551 \u2013 $75,300[\/latex]<\/td>\r\n[latex]$9,276 \u2013 $37,650[\/latex]<\/td>\r\n[latex]$13,251 \u2013 $50,400[\/latex]<\/td>\r\n<\/tr>\r\n
25%<\/th>\r\n[latex]$37,651 \u2013 $91,150[\/latex]<\/td>\r\n[latex]$75,301 \u2013 $151,900[\/latex]<\/td>\r\n[latex]$37,651 \u2013 $75,950[\/latex]<\/td>\r\n[latex]$50,401 \u2013 $130,150[\/latex]<\/td>\r\n<\/tr>\r\n
28%<\/th>\r\n[latex]$91,151 \u2013 $190,150[\/latex]<\/td>\r\n[latex]$151,901 \u2013 $231,450[\/latex]<\/td>\r\n[latex]$75,951 \u2013 $115,725[\/latex]<\/td>\r\n[latex]$130,151 \u2013 $210,800[\/latex]<\/td>\r\n<\/tr>\r\n
33%<\/th>\r\n[latex]$190,151 \u2013 $413,350[\/latex]<\/td>\r\n[latex]$231,451 \u2013 $413,350[\/latex]<\/td>\r\n[latex]$115,726 \u2013 $206,675[\/latex]<\/td>\r\n[latex]$210,801 \u2013 $413,350[\/latex]<\/td>\r\n<\/tr>\r\n
35%<\/th>\r\n[latex]$413,351 \u2013 $415,050[\/latex]<\/td>\r\n[latex]$413,351 \u2013 $466,950[\/latex]<\/td>\r\n[latex]$206,676 \u2013 $233,475[\/latex]<\/td>\r\n[latex]$413,351 \u2013 $441,000[\/latex]<\/td>\r\n<\/tr>\r\n
39.6%<\/th>\r\n[latex]$415,051+[\/latex]<\/td>\r\n[latex]$466,951+[\/latex]<\/td>\r\n[latex]$233,476+[\/latex]<\/td>\r\n[latex]$441,001+[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"

Some functions come in pieces. In this section, we will learn about how to define and graph functions that are essentially collections of discrete pieces. Examples of something defined this way include designing the profile of a car, figuring out your mobile phone plan, and calculating\u00a0income tax rates. For example, your tax rate depends on your income and is the same for a range of incomes as shown in the table below:<\/p>\n\n\n\n\n\n\n\n\n\n\n
Marginal Tax Rate<\/th>\nSingle Taxable Income<\/th>\nMarried Filing Jointly or Qualified Widow(er) Taxable Income<\/th>\nMarried Filing Separately Taxable Income<\/th>\nHead of Household Taxable Income<\/th>\n<\/tr>\n
10%<\/th>\n[latex]$0 \u2013 $9,275[\/latex]<\/td>\n[latex]$0 \u2013 $18,550[\/latex]<\/td>\n[latex]$0 \u2013 $9,275[\/latex]<\/td>\n[latex]$0 \u2013 $13,250[\/latex]<\/td>\n<\/tr>\n
15%<\/th>\n[latex]$9,276 \u2013 $37,650[\/latex]<\/td>\n[latex]$18,551 \u2013 $75,300[\/latex]<\/td>\n[latex]$9,276 \u2013 $37,650[\/latex]<\/td>\n[latex]$13,251 \u2013 $50,400[\/latex]<\/td>\n<\/tr>\n
25%<\/th>\n[latex]$37,651 \u2013 $91,150[\/latex]<\/td>\n[latex]$75,301 \u2013 $151,900[\/latex]<\/td>\n[latex]$37,651 \u2013 $75,950[\/latex]<\/td>\n[latex]$50,401 \u2013 $130,150[\/latex]<\/td>\n<\/tr>\n
28%<\/th>\n[latex]$91,151 \u2013 $190,150[\/latex]<\/td>\n[latex]$151,901 \u2013 $231,450[\/latex]<\/td>\n[latex]$75,951 \u2013 $115,725[\/latex]<\/td>\n[latex]$130,151 \u2013 $210,800[\/latex]<\/td>\n<\/tr>\n
33%<\/th>\n[latex]$190,151 \u2013 $413,350[\/latex]<\/td>\n[latex]$231,451 \u2013 $413,350[\/latex]<\/td>\n[latex]$115,726 \u2013 $206,675[\/latex]<\/td>\n[latex]$210,801 \u2013 $413,350[\/latex]<\/td>\n<\/tr>\n
35%<\/th>\n[latex]$413,351 \u2013 $415,050[\/latex]<\/td>\n[latex]$413,351 \u2013 $466,950[\/latex]<\/td>\n[latex]$206,676 \u2013 $233,475[\/latex]<\/td>\n[latex]$413,351 \u2013 $441,000[\/latex]<\/td>\n<\/tr>\n
39.6%<\/th>\n[latex]$415,051+[\/latex]<\/td>\n[latex]$466,951+[\/latex]<\/td>\n[latex]$233,476+[\/latex]<\/td>\n[latex]$441,001+[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\t\t\t
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Candela Citations<\/h3>\n\t\t\t\t\t
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