Question

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.

Answer 1

The given function is

f(x)= 3
`\sqrt\left- |x  \right-2 |+6` ⇒[Absolute value function]

F(x)= 1. 3
`\sqrt {-(x-2)+6}` =
`3\sqrt {-x+2+6}=3√(-x+8)` when (x-2≥0→x≥2) ⇒[ Piecewise function]

2.
`3√(-[-(x-2)]+6)=3√(x-2+6)=3√(x+4)` 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.