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Other Graphs Other Graphs - Cubic, Reciprocal, Exponential
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
Plot y = x³: at x = −2, −1, 0, 1, 2 you get y = −8, −1, 0, 1, 8. It passes through the origin and can cross the x-axis up to three times. If a is negative the S is flipped.
For y = 6/x: x = 1, 2, 3 give y = 6, 3, 2. As x grows, y nears 0; as x nears 0, y shoots up. The x-axis and y-axis are asymptotes. Find k from any point: (3, 4) gives k = 12.
For y = 2ˣ: x = 0, 1, 5 give y = 1, 2, 32. It hugs the x-axis on the left, never crossing it. If a is between 0 and 1 it decays instead, falling toward 0.
Crosses the y-axis at 1 and never the x-axis: exponential. Two separate branches in opposite corners: reciprocal. One continuous S through three quadrants: cubic.
Hard words & meanings
| cubic | a curve from an equation whose highest power of x is 3 |
| reciprocal | the graph of y = k/x, made of two separate branches |
| exponential | a curve y = aˣ where x is the power; it grows or decays fast |
| asymptote | a line that a curve approaches ever more closely but never touches |
| root | a value of x where the curve crosses the x-axis (y = 0) |
| y-intercept | the y-value where the curve crosses the y-axis (x = 0) |
| decay | an exponential that falls toward zero as x increases (0 < a < 1) |
| branch | one of the two separate parts of a reciprocal curve |
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