# 数学代写|微积分代写Calculus代考|MATH265

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## 数学代写|微积分代写Calculus代考|The Graph of an Equation

In Section 1.1, you used a coordinate system to represent graphically the relationship between two quantities. There, the graphical picture consisted of a collection of points in a coordinate plane.

Frequently, a relationship between two quantities is expressed as an equation in two variables. For instance, $y=7-3 x$ is an equation in $x$ and $y$. An ordered pair $(a, b)$ is a solution or solution point of an equation in $x$ and $y$ if the equation is true when $a$ is substituted for $x$ and $b$ is substituted for $y$. For instance, $(1,4)$ is a solution of $y=7-3 x$ because $4=7-3(1)$ is a true statement.
In this section you will review some basic procedures for sketching the graph of an equation in two variables. The graph of an equation is the set of all points that are solutions of the equation.
Example 1 Determining Solutions
Determine whether (a) $(2,13)$ and (b) $(-1,-3)$ are solutions of the equation $y=10 x-7$.
Solution
a.
\begin{aligned} y & =10 x-7 & & \text { Write original equation. } \ 13 & \stackrel{?}{=} 10(2)-7 & & \text { Substitute } 2 \text { for } x \text { and } 13 \text { for } y . \ 13 & =13 & & (2,13) \text { is a solution. } \checkmark \end{aligned}
Because the substitution does satisfy the original equation, you can conclude that the ordered pair $(2,13)$ is a solution of the original equation.
b.
Write original equation.
\begin{aligned} & -3 \stackrel{?}{=} 10(-1)-7 \ & -3 \neq-17 \end{aligned}
$$\text { Substitute }-1 \text { for } x \text { and }-3 \text { for } y \text {. }$$
$$(-1,-3) \text { is not a solution. }$$
Because the substitution does not satisfy the original equation, you can conclude that the ordered pair $(-1,-3)$ is not a solution of the original equation.

## 数学代写|微积分代写Calculus代考|Intercepts of a Graph

It is often easy to determine the solution points that have zero as either the $x$-coordinate or the $y$-coordinate. These points are called intercepts because they are the points at which the graph intersects or touches the $x$ – or $y$-axis. It is possible for a graph to have no intercepts, one intercept, or several intercepts, as shown in Figure 1.19.

Note that an $x$-intercept can be written as the ordered pair $(x, 0)$ and a $y$-intercept can be written as the ordered pair $(0, y)$. Some texts denote the $x$-intercept as the $x$-coordinate of the point $(a, 0)$ [and the $y$-intercept as the $y$-coordinate of the point $(0, b)]$ rather than the point itself. Unless it is necessary to make a distinction, we will use the term intercept to mean either the point or the coordinate.
Finding Intercepts

To find $x$-intercepts, let $y$ be zero and solve the equation for $x$.

To find $y$-intercepts, let $x$ be zero and solve the equation for $y$.
Example 4 Finding $x$ – and $y$-Intercepts
Find the $x$ – and $y$-intercepts of the graph of $y=x^3-4 x$.
Solution
Let $y=0$. Then
$$0=x^3-4 x=x\left(x^2-4\right)$$
has solutions $x=0$ and $x= \pm 2$.
$$x \text {-intercepts: }(0,0),(2,0),(-2,0)$$
Let $x=0$. Then
$$y=(0)^3-4(0)$$
has one solution, $y=0$.
$y$-intercept: $(0,0) \quad$ See Figure 1.20.

## 数学代写|微积分代写Calculus代考|The Graph of an Equation

a。
\begin{aligned} y & =10 x-7 & & \text { Write original equation. } \ 13 & \stackrel{?}{=} 10(2)-7 & & \text { Substitute } 2 \text { for } x \text { and } 13 \text { for } y . \ 13 & =13 & & (2,13) \text { is a solution. } \checkmark \end{aligned}

b。

\begin{aligned} & -3 \stackrel{?}{=} 10(-1)-7 \ & -3 \neq-17 \end{aligned}
$$\text { Substitute }-1 \text { for } x \text { and }-3 \text { for } y \text {. }$$
$$(-1,-3) \text { is not a solution. }$$

## 数学代写|微积分代写Calculus代考|Intercepts of a Graph

$$0=x^3-4 x=x\left(x^2-4\right)$$

$$x \text {-intercepts: }(0,0),(2,0),(-2,0)$$

$$y=(0)^3-4(0)$$

$y$ -intercept: $(0,0) \quad$参见图1.20。

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。