Julia is an intern at an architecture firm. She is given an assignment to create a bell-shaped structure that is symmetrical. She writes the function f(x)=3 squareroot -|x-2|+6 to model the structure. Find the piecewise function that matches this absolute value function. Then, graph the function using a graphing calculator and describe what you see.

Accepted Solution

Answer:The given function isf(x)= 3 [tex]\sqrt\left- |x  \right-2 |+6[/tex] ⇒[Absolute value function]F(x)=  1.  3[tex]\sqrt {-(x-2)+6}[/tex] =[tex]3\sqrt {-x+2+6}=3\sqrt{-x+8}[/tex] when (x-2≥0→x≥2) ⇒[ Piecewise function]    2. [tex]3\sqrt{-[-(x-2)]+6}=3\sqrt{x-2+6}=3\sqrt{x+4}[/tex] when [ x-2<0→x<2]⇒[ Piecewise function]We see there is a shape which is is in the form of dome,point of intersection  of two curves being (2,7.348), symmetrical on both side of line x=2.