Sketching absolute value, reciprocal and rational graphs

What this note covers

1. Sketching |f(x)|
2. Sketching f(|x|)
3. Reciprocal graphs
4. Oblique asymptotes
5. Removable discontinuities
6. Repeated denominator factors
7. Absolute-value transformations with piecewise graphs and exact turning points
8. Rational-graph anatomy: asymptotes, holes, signs and exact range

8 sections · 10 key terms & formulas · 6 common mistakes