# 计算机代写|计算机图形学代写computer graphics代考|CSCl420

## 计算机代写|计算机图形学代写computer graphics代考|Function Domains and Ranges

The following descriptions of domains and ranges only apply to functions with one independent variable: $f(x)$.
Returning to the above function:
$$y=f(x)=3 x^2+2 x+4$$
the independent variable $x$, can take on any value from $-\infty$ to $\infty$, which is called the domain of the function. In this case, the domain of $f(x)$ is the set of real numbers $\mathbb{R}$. The notation used for intervals, is also used for domains, which in this case is
$$]-\infty, \infty[$$
and is open, as there are no precise values for $-\infty$ and $\infty$.
As the independent variable takes on different values from its domain, so the dependent variable, $y$ or $f(x)$, takes on different values from its range. Therefore, if the domain of the linear function $f(x)=3 x+4$ is $[-4,4]$, the range of $f(x)$ is calculated by finding $f(-4)$ and $f(4)$ :
$$\begin{gathered} f(-4)=-12+4=-8 \ f(4)=12+4=16 \end{gathered}$$
and the range is $[-4,4]$.
Although calculating the range of linear functions is simple, other types of functions require a knowledge of calculus.
The domain of $\log x$ is
$$] 0, \infty[$$
which is open, because $x \neq 0$. Whereas, the range of $\log x$ is
$$]-\infty, \infty[\text {. }$$
The domain of $\sqrt{x}$ is
$$[0, \infty[$$

## 计算机代写|计算机图形学代写computer graphics代考|Odd and Even Functions

An odd function satisfies the condition:
$$f(-x)=-f(x)$$ where $x$ is located in a valid domain. Consequently, the graph of an odd function is symmetrical relative to the origin. For example, $\sin (\theta)$ is odd because
$$\sin (-\theta)=-\sin \theta$$
as illustrated in Fig. 3.6. Other odd functions include:
\begin{aligned} &f(x)=a x \ &f(x)=a x^3 \end{aligned}
An even function satisfies the condition:
$$f(-x)=f(x)$$
where $x$ is located in a valid domain. Consequently, the graph of an even function is symmetrical relative to the $f(x)$ axis. For example, $\cos \theta$ is even because
$$\cos (-\theta)=\cos \theta$$
as illustrated in Fig. 3.7. Other even functions include:
\begin{aligned} &f(x)=a x^2 \ &f(x)=a x^4 \end{aligned}

# 计算机图形学代考

## 计算机代写|计算机图形学代写computer graphics代考|Function Domains and Ranges

$$y=f(x)=3 x^2+2 x+4$$

$$]-\infty, \infty[$$

$$f(-4)=-12+4=-8 f(4)=12+4=16$$

$$] 0, \infty[$$

$$]-\infty, \infty[\text {. }$$

$$[0, \infty[$$

## 计算机代写|计算机图形学代写computer graphics代考|Odd and Even Functions

$$f(-x)=-f(x)$$

$$\sin (-\theta)=-\sin \theta$$

$$f(x)=a x \quad f(x)=a x^3$$

$$f(-x)=f(x)$$

$$\cos (-\theta)=\cos \theta$$

$$f(x)=a x^2 \quad f(x)=a x^4$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: