Precalculus functions OR Statistics: data ethics & displays

Precalculus path: analyze functions (domain, range, symmetry, intervals of increase, composition). Statistics path: choose honest data displays and handle data ethically. Precalc: even functions satisfy f(−x) = f(x) (symmetric about the y-axis); odd functions satisfy f(−x) = −f(x) (symmetric about the origin). Stats: choose displays by data type — bar charts for categories; histograms, dotplots, and boxplots for quantitative data. Stats: ethical data use means informed consent, privacy, honest axes, and reporting all results, not just favorable ones. Precalc: f(x) = x³ − x: f(−x) = −x³ + x = −f(x), so f is odd. g(x) = x² + 4 is even. f is increasing where its graph rises; for y = x², that is (0, ∞). Stats: a bar chart with a y-axis starting at 980 makes 990 vs. 1,000 look like a doubling; starting at 0 shows a 1% difference. Collecting student data requires consent and removing names (de-identifying). Precalc: classify h(x) = x⁴ − 3x². h(−x) = (−x)⁴ − 3(−x)² = x⁴ − 3x². That equals h(x). h is even. (Stats path: name the variable type, pick a display, check the axes, and state one ethical safeguard.) Precalc: classify k(x) = x³ + 1 and find its domain and range. Stats: choose and justify a display for "favorite streaming service" and for "minutes of daily screen time." Usual mistake: Precalc: assuming every function is even or odd. Stats: using a pie chart for quantitative data, or cropping an axis to dramatize change.