Unit 7: Absolute Value & Reciprocal Functions (Math 20-1)
Absolute value functions & equations; transformations; reciprocal functions, domains & asymptotes; applications.
\(y=a|x-h|+k\)
Piecewise
Reflections & Stretches
Reciprocal \(y=\frac{1}{f(x)}\)
Asymptotes
Restrictions
What You Should Be Able To Do
- Model and graph \(y=a|x-h|+k\); identify vertex, axis, intercepts, domain/range; write piecewise form.
- Solve absolute value equations \(|ax+b|=c\) and interpret solutions.
- Graph and analyze reciprocal functions \(y=\dfrac{1}{f(x)}\): domain restrictions, vertical/horizontal asymptotes, intercepts.
- Describe transformations and solve applied problems using absolute value or reciprocal models.
Progress autosaves to this device.
Video Library
Graphing \(y=a|x-h|+k\)
Vertex, slopes, domain/range, transformations.
youtube.com – “graph absolute value function transformations”Solving \(|ax+b|=c\)
Two linear cases, extraneous checks if needed.
youtube.com – “solve absolute value equations algebraically”Reciprocal Functions & Asymptotes
Vertical/horizontal asymptotes, restrictions, key points.
youtube.com – “reciprocal functions asymptotes domain range”Applications & Modelling
Context problems using |x| and reciprocal models.
youtube.com – “modelling with absolute value and reciprocal functions”Interactive Tools
Absolute Value Explorer \(y=a|x-h|+k\)
Solve \(|ax+b|=c\)
Hyperbola Explorer \(y=\dfrac{A}{x-h}+k\)
Reciprocal of \(f(x)\): plot \(f(x)\) and \(\frac{1}{f(x)}\)
Unit 7 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: graph \(y=2|x-3|-5\); solve \(|3x-7|=11\); graph \(y=\frac{5}{x+2}-1\); sketch \(y=\frac{1}{x^2-4}\) with asymptotes.