M 2.4 Discussion: MAIN POST Daphne Beltz Natural Exponential function when x 4- 2 Natural Logarithmic function When www X Z - Z My piecewise function is x + 2 f (x) = 7+ 1 X 2 - 2 ( In ( x + 3 ) + 2 , x2 - 2 My piecewise function annotated in Desmos is as follows : ( x + 2 + 1 x 2 2 : In ( x + 3 ) + 2 8 Finding |lim f ( x) , using the analytical approach , I X - - 2 x + 2 will plug in - 2 into y = e + 1 since we will be approaching - 2 from the left . lim f ( x = e 12 - 2 + 2 x - - 2 - Finding lim f ( x ), using the analytical approach , I will plug in -2 into 4 = In ( x + 3 ) +2 since we will be approaching - 2 from the right . lim s( x) - In ( - 2 + 3 ) + 2 X - - 2 + In ( 1 ) + 2 0 + 2 Finding lim X -7 2 f (x ) , using the analytical approch, we have determined that lim . The p ( x ) = J ( - 2 ) = 2. x-7 - 2 - Therefore , the 1im f ( x) = 2) X - - 2