# Maths: 基本初等函数及其图像 Elementary Functions Graphs

### Common Functions Reference

https://www.mathsisfun.com/sets/functions-common.html

Here are some of the most commonly used functions, and their graphs:

### Which functions are called elementary?

In our calculus course, we are going to deal mostly with elementary functions.

They are

- power functions
- exponential functions
- logarithmic functions
- trigonometric functions
- inverse trigonometric functions

and their sums, differences, products, quotients, and compositions.

### Parent Functions And Their Graphs

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent. Scroll down the page for more examples and solutions.

The following table shows the transformation rules for functions. Scroll down the page for examples and solutions on how to use the transformation rules.

#### Parent Functions And Their Graphs - How To Graph Elementary Functions?

In math, we often encounter certain elementary functions. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. It is important to recognize the graphs of elementary functions, and to be able to graph them ourselves. This will be especially useful when doing transformations.

#### Basic Graphs That Every Algebra Student Should Know

Basic graphs that are useful to know for any math student taking algebra or higher.

y = mx + b (linear function)

y = x^{2} (quadratic)

y = x^{3} (cubic)

y = x^{5}

y = |x| (absolute)

y = √x (square root)

y = 1/x (reciprocal)

y = 1/x^{2}

y = log_{b}(x) for b > 1

y = a^{x} for a > 1 (exponential)

y = a^{x} for 0 < a < 1

#### The Graphs Of Six Basic Functions That You Should Know

f(x) = x

f(x) = x^{2}

f(x) = x^{3}

f(x) = √x

f(x) = cube root(x)

f(x) = |x|

#### 7 Parent Functions With Equations, Graphs, Domain, Range And Asymptotes

y = x

y = x^{2}

y = √x

y = x^{3}

y = 1/x

y = 1/x^{2}

y = |x|

#### Exploring Properties Of Parent Functions

In math, every function can be classified as a member of a family. Each member of a family of functions is related to its simpler, or most basic, function sharing the same characteristics. This function is called the parent function.

This lesson discusses some of the basic characteristics of linear, quadratic, square root, absolute value and reciprocal functions.

#### Transformations Of Parent Functions

Learn how to shift graphs up, down, left, and right by looking at their equations.

Vertical Shifts:

f(x) + c moves up,

f(x) - c moves down.

Horizontal Shifts:

f(x + c) moves left,

f(x - c) moves right.