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1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

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1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Mathematics · 术语表

什么是 Affine function？

又称： slope · y-intercept

Definition 67.4 Primary & Middle School Mathematics · 第 67 章 — Linear and Affine Functions

An affine function has the form

f(x) = a x + b ,

where $a$ and $b$ are fixed numbers. Linear functions are the special case $b = 0$ ; constant functions the case $a = 0$ .

示例

Example 67.8

Find the affine function with $f(2) = 7$ and $f(5) = 16$ .

a = \frac{16 - 7}{5 - 2} = \frac93 = 3 ,

then $f(2) = 3 \times 2 + b = 7$ gives $b = 1$ : $f(x) = 3x + 1$ . Check: $f(5) = 15 + 1 = 16$ .

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Definition 4.1 High School Mathematics · 第 4 章 — Reference Functions

An affine function is a function of the form

f(x) = mx + p,

where $m$ and $p$ are fixed real numbers. Its graph is a straight line: $m$ is the slope and $p$ the $y$ -intercept (the line crosses the vertical axis at $(0, p)$ ). When $p = 0$ the function is linear: $f(x) = mx$ expresses proportionality.

Two affine functions: increasing for m = 1/2 > 0, decreasing for m = -1 < 0. Moving one unit to the right changes y by m. — Two affine functions: increasing for $m = \frac12 > 0$ , decreasing for $m = -1 < 0$ . Moving one unit to the right changes $y$ by $m$ .

示例

Example 4.3

Find the affine function whose graph passes through $A(1, 3)$ and $B(4, 9)$ . The slope is

m = \frac{9 - 3}{4 - 1} = \frac{6}{3} = 2 .

Then $f(x) = 2x + p$ , and $f(1) = 3$ gives $2 + p = 3$ , so $p = 1$ : $f(x) = 2x + 1$ . Check with $B$ : $f(4) = 9$ .

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