help would be very much appreciated bc i’m abt to tweak out after answering 50+ questions but this is my last one!! plsss help

help would be very much appreciated bc im abt to tweak out after answering 50 questions but this is my last one plsss help class=
help would be very much appreciated bc im abt to tweak out after answering 50 questions but this is my last one plsss help class=


Answer :

Answer:

[tex]f(x) = \left \{ {{y=\frac{2}{5}(x+5)\ for\ (- \infty, 0) } \atop {y=5-x}\ for\ (4, \infty)} \right.[/tex]

Step-by-step explanation:

[tex]In\ order\ to\ keep\ the\ answer\ simple:\\We'll\ divide\ our\ solution\ into\ 3\ intervals.\\[/tex][tex]In\ the\ interval (- \infty , 0):\\We\ find\ that\ the\ function\ is\ a\ straight\ line\ passing\ through\ the\ points\ (0,2)\\and\ (-5,0).\\Hence, Slope = \frac{y_2 - y_1}{x_2 - x_1} =\frac{0-2}{-5-0} = \frac{2}{5}\\ Using\ the\ point-slope\ formula:\\y-y_0 = m(x-x_0)\\y-0 = \frac{2}{5}(x-(-5))\\ Hence,\\y = \frac{2}{5}(x+5)[/tex]

[tex]In\ the\ Interval\ (0,4):\\The\ graph\ is\ discontinuous\ and\ breaks.[/tex]

[tex]In\ the\ interval (4 , \infty):\\We\ find\ that\ the\ function\ is\ a\ straight\ line\ passing\ through\ the\ points\ (4,1)\\and\ (5,0), although\ (4,1)\ is\ not\ in\ its\ domain.\\Hence, Slope = \frac{y_2 - y_1}{x_2 - x_1} =\frac{0-1}{5-4} = \frac{-1}{1}=-1\\ Using\ the\ point-slope\ formula:\\y-y_0 = m(x-x_0)\\y-0 = -1(x-5)\\ Hence,\\y = 5 - x[/tex]