加拿大12年级数学-笔记 (持续更新)

此笔记的背景

站主是理科生,在中国读大学本科工科,原本数理化都还可以,但是来到北美,专业不对口,毕业后也没又从事专业的工作,一直对工程专业,技术专业有执念,想趁着还不算晚,再去学一门技术工程类的学位便于就业,但是发现数学物理词汇在英文下完全不不熟悉,所以开始了自学之旅。。。

 数学词汇

Inverse function: 反函数

Piece-wise function:分段函数

Parent Function:母函数

Transformed Function: 变换后的函数

Compute if “…” is defined 计算该式子是否有意义

R Stands for real number, (-∞,+∞)是取值范围。

Function notation 函数表达,即将一个函数写成f(X)=的形式

exponential function 指数函数

vertical asymptotes 垂直渐近线

horizontal asymptotes 水平渐近线

converging arrows 汇聚箭头

diverging arrows 分流箭头

symmetric 对称, the graph is symmetric about the y-axis,图像关于Y轴对称。

Absolute value 绝对值

properties of graphs of functions 函数的图像性质

Intervals of increase 递增区间

Intervals of decrease 递减区间

Odd function 奇函数, any function that has rotational symmetry about the origin; 关于远点对称的函数

Even function 偶函数, any function that is symmetric about the y-axis; 关于Y轴对称的函数。

asymptotes 渐近线

continuous function 连续函数

discontinuous function 非连续函数

常见问题,中文解释

  1. Factor each of the following expressions. 分解因式

以上述a问题为例,因式可以写为(x+y)乘(x+y)

2. State the domain and range of each function. 找到一个方程的x取值的职域,也就是domain,range是取值X,得到y的值域。

3. State the transformations that are applied to each parent function,
resulting in the given transformed function. Sketch the graphs of the
parent function and transformed function.

Parent Function是母函数,原函数。Transformed function,变化后的函数。State the transformations that are applied to parent functions,是让考生形容图像函数图像的变化。

例题:

b: one unit to right, and 2 units up.

4. Test whether the equation is a function, using the vertical line test method.

Vertical Line Test

The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of a relation, and then observe the points of intersections.

The vertical line test supports the definition of a function. That is, every �x-value of a function must be paired to a single �y-value. If a vertical line intersects the graph of a relation at exactly one point, it implies that a single �x-value is only paired to a unique value of �y.

On the other hand, if the vertical line intersects the graph more than once, this suggests that a single �x-value is being associated with more than one value of �y. This condition causes the relation to be “disqualified” as a function.

Absolute Value

How could you use transformations to describe the graph of…如何描述一个图像的变化情况。

需要先描述,原函数是什么函数,然后是怎么平移的。

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