6.º a 8.º gradoAnalysisLección disponible
Graphs of change
Reading and sketching graphs that show how one quantity changes with another, such as distance against time, and interpreting steepness as rate of change.
math.analysis.graphs-of-change
Se basa en
Requisitos previos obligatorios, hasta el fondo: 8
Aprenderás a
- Interpret distance–time and other real-world graphs, describing where a quantity increases, decreases or stays constant.
- Compute average rates of change between two points of a graph or table.
- Sketch a graph from a verbal description, and describe a situation from a graph.
Definición
- The average rate of change of y between x = a and x = b is (y(b) − y(a))/(b − a).
- A graph is increasing on an interval if y gets larger whenever x gets larger within that interval.
Teorema
- On a graph of distance from the start against time, the slope of a segment is the average velocity over that interval (negative when moving back towards the start); it equals the average speed when there is no turning back.
- A horizontal segment means the quantity is not changing.
- Two situations can have the same average rate over an interval but behave differently within it.
Errores frecuentes
- Reading a distance–time graph as a picture of the path travelled, such as a hill.
- Thinking a steeper graph means a larger quantity rather than a faster change.
Conduce a
Descubrimientos opcionales
- Introductory calculus Shrinking the interval turns an average rate of change into an instantaneous rate: the derivative.
Lecturas complementarias
- Malcolm Swan and the Shell Centre for Mathematical Education, The Language of Functions and Graphs (1985)
- I. M. Gelfand, E. G. Glagoleva and E. E. Shnol, Functions and Graphs (1969)