range of 2cos(x)+1

{ "query": { "display": "range $$2\\cos\\left(x\\right)+1$$", "symbolab_question": "FUNCTION#range 2\\cos(x)+1" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "range", "default": "-1\\le f(x)\\le 3", "interval": "[-1,3]", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Range of $$2\\cos\\left(x\\right)+1:{\\quad}-1\\le\\:f\\left(x\\right)\\le\\:3$$", "steps": [ { "type": "definition", "title": "Function range definition", "text": "The set of values of the dependent variable for which a function is defined" }, { "type": "step", "primary": "The range of the basic $$\\cos\\:$$function is $$-1\\le\\:\\cos\\left(x\\right)\\le\\:1$$", "result": "-1\\le\\:\\cos\\left(x\\right)\\le\\:1" }, { "type": "step", "primary": "Multiply the edges of the range by: $$2$$", "result": "-2\\le\\:2\\cos\\left(x\\right)\\le\\:2" }, { "type": "step", "primary": "Add to the edges of the range: $$1$$", "result": "-1\\le\\:2\\cos\\left(x\\right)+1\\le\\:3" }, { "type": "step", "primary": "Therefore the range is", "result": "-1\\le\\:f\\left(x\\right)\\le\\:3" } ], "meta": { "solvingClass": "Function Range" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "2\\cos(x)+1" }, "showViewLarger": true } }, "meta": { "showVerify": true } }