Chapter 6 - Transformations of Functions and Their Graphs - 6.1 Shifts, Reflections, and Symmetry - Exercises and Problems for Section 6.1 - Skill Refresher - Page 240: S10

(a) $f(-x)=-\frac{3x^3}{x^2-1}$ (b) $-f(x)=-\frac{3x^3}{x^2-1}$

(a) Replace $x$ with $-x$ to get $$f(-x)=\frac{3(-x)^3}{(-x)^2-1}=-\frac{3(-1)^3x^3}{(-1)^2x^2-1}=-\frac{3x^3}{x^2-1}$$ (b) Multiply $f(x)$ by $-1$ to get $-f(x)=-\frac{3x^3}{x^2-1}$.