Differential calculus - Functions and their graphs

Functions : f,g,y,u,v
Argument (independent variable ) : x
Real number : a,b,c,d
Natural number : n
Angle : $\alpha$
Inverse function : $f^{-1}$

1. Even Function
$f(-x)=f(x)$
2. Odd Function
$f(-x)=-f(x)$
3. Periodic Function
$f(x+nT)=f(x)$
4. Inverse Function
$y=f(x)$ is any function , $x=g(y)$ or $y=f^{-1}(x)$ is its inverse function.
5. Composite Function
$y=f(u),u=g(x), y=f(g(x))$ is a composite function .
6. Linear Function
$y=ax+b, x \in R , a = \tan \alpha$ is the slope of the line , b is the y-intercept.
$y=x^2, x \in R.$
8. $y=ax^2+bx+c , x \in R.$
9. Cubic Function
$y=x^2 , x \in R.$
10. $y=ax^3+bx^2+cx+d \;, x \in R.$
11. Power Function
$y=x^n , n \in N.$

12. Square Root Function
$y= \sqrt {x} , x \in [0,\infty).$
13. Exponential Functions
$y=a^x, a>0, a \ne 1,$
$y=e^x$ if a=e , e=2.71828182846.....
14. Logarithmic Functions
$y=log_ax , x \in (0, \infty), a>0, a\ne 1,$
$y=Inx$ if a=e , x >0.
15. Hyperbolic Sine Function
$y=sinh\,x, sinh\,x={e^x-e^{-x} \over 2}, x \in R.$
16. Hyperbolic Cosine Function
$y= cosh \,x, cosh\; x= {e^x+e^{-x} \over 2}, x \in R.$
17. Hyperbolic Tangent Function
$y=tanh\, x , y=tanh\, x= {sinh \, x \over cosh \, x}={e^x-e^{-x} \over e^x-e^{-x}}$,$x \in R.$
18. Hyperbolic Cotangent function
$y= coth \, x, y=coth \, x={cosh \, x \over sinh \, x}={e^x+e^{-x} \over e^x-e^{-x}}$,$x \in R, x\ne 0.$
19. Hyperbolic Secant Function
$y=sech\, x, y=sech \, x= {1 \over cosh \, x}={2 \over e^x+e^{-x}},x \in R.$
20. Hyperbolic Secant Function
$y=srch \, x,y=sech \, x= {1 \over cosh \,x}={2 \over e^x+e^{-x}}, x \in R.$
21. Hyperbolic Cosecant Function
$y=csch \, x, y= csch \, x ={1 \over sinh \, x}={2 \over e^x-e^{-x}}, x \in R, x \ne 0.$
22. Inverse Hyperbolic Sine Function
$y=arcsinh \, x , x \in R.$
23. Inverse Hyperbolic Cosine Function
$y=arccosh \, x , x \in [1 , \infty ).$
24. Inverse Hyperbolic Tangent Function
$y=arctanh \, x , x \in (-1,1).$
25. Inverse Hyperbolic Cotangent Function
$y=arccoth \, x , x \in (- \infty ,-1) \cup (1, \infty ).$
26. Inverse Hyperbolic Secant Function
$y=arcsech \, x , x \in (0,1].$
27. Inverse Hyperbolic Cosecant Function
$y=arccsch \, x , x \in R , x \ne 0.$