---
# System prepended metadata

title: Sketch a Function
tags: [Calculus]

---

# Sketch a Function
###### tags:`Calculus`
### Step1:
#### Find Domain, Symmetry(odd or even) ,Periodic(周期性)
#### Intercept f(0)(截距), Asymptotes(vertical, horizontal , slant)
### Step2:
#### Find f'(x)
#### Increasing/Decreasing Test , Critical Point, Local Extreme
### Step3:
#### Find f''(x)
#### Concavity Test , Inflection Point
## Asymptotes
$$
The\;graph\;of\;f\;has\;an\;asymptote\\if\;\lim_{x\rightarrow\infty}\lbrack f(x)-(mx+b)\rbrack=0\;for\;some\;m,b\;\in\mathbb{R}\\Note:\left\{\begin{array}{l}m=0,\;horizontal\;asymptote\\m\neq0,\;slant\;asymptote\end{array}\right.\\The\;graph\;of\;f\;has\;an\;asymptote\Leftrightarrow\lim_{x\rightarrow\infty}\frac{f(x)}x=m\;,\;\lim_{x\rightarrow\infty}(f(x)-mx)=b
$$