Av Robert Schrader Uppdaterad 30 augusti 2022
All algebraic equations can be represented graphically on a coordinate plane, which helps to visualize both their domain and range. The domain consists of all possible x‑values, while the range consists of all possible y‑values. Understanding these concepts is essential for analyzing the behavior of algebraic functions.
Välj en exempelekvation att analysera. Tänk till exempel på y = x² + 5 .
Evaluate the function at several x‑values:-10, 0, 6, and 8. The resulting y‑values are 105, 5, 41, and 69. Observing these results reveals a clear pattern.
Define the range:the set of all possible y‑values. För y = x² + 5 , the smallest y is 5, occurring at x =0. Therefore the range is y ≥ 5.
Graph the function using a graphing calculator to confirm the analysis. The parabola reaches its minimum at y =5 and extends infinitely upward, confirming that no y‑values below 5 exist.
Apply the same process to additional functions:y = x + 10 , y = x³ – 20 och y = 3x² – 5 . The first two functions have range all real numbers, while the third has range y ≥ –5.
