Linear and Quadratic Graphs: A solid review of straight lines before moving into the world of Parabolas. Students master the three forms of quadratic equations—expanded, factored, and vertex form—and learn how to identify turning points, axes of symmetry, and intercepts.
The Power of Transformations: Teaches the "translations" of graphs. Students learn how to shift functions vertically and horizontally, and how to reflect or stretch them by altering the constants within the equation ($y = a(x - h)^2 + k$).
Cubic and Exponential Functions: Explores the unique shapes of "S-curves" (cubics) and the rapid growth or decay of exponential graphs. Students practice identifying key features such as points of inflection and horizontal asymptotes.
Hyperbolas and Circles: Introduces more complex coordinate geometry, including the reciprocal function ($y = 1/x$) and the standard equation for a circle centered at $(h, k)$. Students learn to identify vertical asymptotes and calculate radii.
Piecewise Functions: Teaches how to construct a "hybrid" graph made of different functions over specific domains. This is a critical skill for modeling real-life situations where a rule change occurs (e.g., a taxi fare or a water tank filling at different rates).
Logarithmic Graphs: An introduction to the inverse of exponential functions. Students learn the shape and properties of $y = \log_b(x)$, focusing on their vertical asymptotes and $x$-intercepts.
Modeling Real-World Scenarios: Practical applications where students must choose the correct type of function to fit a set of data points—whether it’s the path of a projectile, the cooling of a liquid, or the growth of a population.
Using Technology (Calculators and Desmos): Provides guidance on using graphic calculators and online graphing tools to verify equations, find points of intersection, and analyze key features of complex functions.
Achievement, Merit, and Excellence Scaffolding: Tasks are designed to build progressively. Achievement focuses on drawing and identifying standard graphs, while Excellence requires students to form complex equations from scratch and provide high-level justifications for their models.
Step-by-Step Worked Examples: Includes detailed exemplars that show how to accurately plot points and clearly label axes and key features—essential for gaining full credit in NCEA assessments.
Full Answer Appendix: Features all graphs and numerical solutions at the back of the book, allowing students to check their work for accuracy and symmetry.
Glossary of Graphical Terms: A guide to essential vocabulary—such as Asymptote, Domain, Range, Vertex, and Reciprocal—ensuring students use the correct mathematical terminology in their assessments.