1.1.1 Identify variables: Situation 1 (Linear): - Independent variable: number of kilometres driven, $x$. - Dependent variable: total rental cost in Rands, $f(x)$. Situation 2 (Non-linear): - Independent variable: radius of the circle, $r$. - Dependent variable: area of the circle, $A$. 1.1.2 Write function rules: Situation 1: - Rental cost function: $$f(x) = 230 + 4.30x$$ where $x$ is kilometres driven. Situation 2: - Area of circle function: $$A(r) = \pi r^2$$ 1.1.3 Create tables: Situation 1: | $x$ (km) | $f(x)$ (cost) | | --- | --- | | 0 | $230 + 4.30 \times 0 = 230$ | | 10 | $230 + 4.30 \times 10 = 230 + 43 = 273$ | | 25 | $230 + 4.30 \times 25 = 230 + 107.5 = 337.5$ | | 50 | $230 + 4.30 \times 50 = 230 + 215 = 445$ | Situation 2: | $r$ (radius) | $A(r)$ (area) | | --- | --- | | 1 | $\pi \times 1^2 = \pi \approx 3.14$ | | 2 | $\pi \times 2^2 = 4\pi \approx 12.57$ | | 3 | $\pi \times 3^2 = 9\pi \approx 28.27$ | | 4 | $\pi \times 4^2 = 16\pi \approx 50.27$ | 1.1.4 Sketch graphs: - For Situation 1, plot $f(x) = 230 + 4.30x$ on axes with $x$ as kilometres (independent) and $f(x)$ as cost (dependent). - For Situation 2, plot $A(r) = \pi r^2$ with $r$ as radius (independent) and $A(r)$ as area (dependent). Both graphs show how dependent variables increase with the independent variable, linear for Situation 1 and quadratic for Situation 2.