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.
  7. Quadratic Function 
    \(y=x^2, x \in R.\)
  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 
    \(y=arccsch \, x , x \in R , x \ne 0.\)