Subjects mathematics

Functions Cityscape D70423

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1. The problem is to create a cityscape design using various mathematical functions to represent different architectural elements. 2. We use different types of functions for different parts: - Building Walls: Linear or Constant Functions, e.g., $y = mx + b$ or $y = c$ - Roofs/Arches: Quadratic or Absolute Value Functions, e.g., $y = ax^2 + bx + c$ or $y = a|x| + b$ - Hills/Riverbanks: Square Root Functions, e.g., $y = a\sqrt{x - h} + k$ - Complex Structures/Steps: Piecewise Functions, e.g., $y = \begin{cases} f_1(x), & x < a \\ f_2(x), & x \geq a \end{cases}$ - Overhead Wires/Unique Structures: Rational Functions, e.g., $y = \frac{p(x)}{q(x)}$ 3. Sketch your cityscape on graph paper with the x-axis as ground level and y-axis as vertical centerline. 4. Label each feature with the function type and write the corresponding equations. 5. Use a digital tool like Desmos or GeoGebra to graph each function and create the cityscape. 6. Group equations by their location in the cityscape and function type. 7. Be creative with colors and function variations. 8. Decide your partner for the task. 9. Submit the initial sketch, equations, digital cityscape printout, and rubric printout by June 17, 2026, 3pm. This task combines understanding of function types, graphing skills, and creativity to produce a structured cityscape design.