कक्षा 6–8Analysisनियोजित
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
इस विषय का पाठ अभी लिखा नहीं गया है। नीचे दी गई रूपरेखा पाठ्यक्रम-मानचित्र का हिस्सा है और इसकी समीक्षा नहीं हुई है।
इस पर आधारित
8 अनिवार्य पूर्वापेक्षाएँ (बिल्कुल नीचे तक)
आप सीखेंगे
- 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.
परिभाषा
- 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.
प्रमेय
- On a distance–time graph, the slope of a segment is the average speed over that time interval.
- 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.
आम भ्रांतियाँ
- 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.
आगे ले जाता है
वैकल्पिक खोजें
- Introductory calculus Shrinking the interval turns an average rate of change into an instantaneous rate: the derivative.