Parent function: Reciprocal-squared, f ( x ) = 1 x 2 f(x)= x 2 1 Transformations from the parent: shifted down 1 unit Model for the red curve: y = 1 x 2 1 y= x 2 1 1 (Vertical asymptote at x = 0 x=0; horizontal asymptote at y = 1 y=1.) Domain / Range: Domain: ( , 0 ) ( 0 , ) (,0)(0,) Range: ( 1 , ) (1,) Yintercept: none (function is undefined at x = 0 x=0) Zeros: solve 1 x 2 1 = 0 x = 1 x 2 1 1=0x=1. Intercepts: ( 1 , 0 ) (1,0) and ( 1 , 0 ) (1,0) Symmetry: about the yaxis; even function because f ( x ) = f ( x ) f(x)=f(x) End behavior: As x x, f ( x ) 1 f(x)1 (approaches the horizontal asymptote). As x 0 x0 , f ( x ) + f(x)+. Intervals of increasing/decreasing/constant: Increasing on ( , 0 ) (,0); decreasing on ( 0 , ) (0,); constant: none. Verify