range of log_{4}(x+4)-4

{ "query": { "display": "range $$\\log_{4}\\left(x+4\\right)-4$$", "symbolab_question": "FUNCTION#range \\log_{4}(x+4)-4" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "range", "default": "-\\infty <f(x)<\\infty ", "interval": "(-\\infty ,\\infty )", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Range of $$\\log_{4}\\left(x+4\\right)-4:{\\quad}-\\infty\\:<f\\left(x\\right)<\\infty\\:$$", "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 a logarithmic function of the form $$c\\cdot\\log\\left(ax+b\\right)+k\\:$$is all the real numbers", "result": "-\\infty\\:<f\\left(x\\right)<\\infty\\:" } ], "meta": { "solvingClass": "Function Range" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\log_{4}(x+4)-4" }, "showViewLarger": true } }, "meta": { "showVerify": true } }